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How would I solve for x?



Step 1. Multiply to get rid of the parenthesis.



Step 2. Combine x-terms



Step 3. Subtract 24 from both sides of the equation





Step 4. Divide by 3 to both sides of the equation





Step 5. Substitute into the original equation to check solution.





which is a true statement.

Step 6. ANSWER: Solution is .

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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The perimeter of a rectangle is 106 inches. The length exceeds the width by 45 inches. Find the length and the width.

The length is 49 inches.

(Type an integer or a decimal)

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let w+45 be the length

Step 4. Then, P=w+w+w+45+w+45=106.

Step 5. Solving yields the following steps



Subtract 90 form both sides of the equation





Divide by 4 to both sides of the equation.





For , then and check which is a true statement.

Step 6. ANSWER: The length is 49 inches.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Dr J

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Problem 1. A SQUARE AND RECTANGLE HAVE EQUAL AREAS. IF THE RECTANGLE IS 36 BY 16, WHAT IS THE SIDE OF A SQUARE?

Step 1. The area of a rectangle A=36*16=576 (area=base*height}}}

Step 2. The square has equal sides where we let s be the side which is equal to the base and height so A=s*s=s^2.

Step 3. The areas are equal in Steps 1 and 2. Then

Step 4. Take the square root to both sides of the equation or .

Step 5. ANSWER: The side of the square is 24.

Problem 2. IN A SOCIAL HALL OF A BUILDING, THERE ARE 150 SEATS ARRANGED IN ROWS WITH 5 MORE SEATS PER ROW THAN THE NUMBER OF ROWS. HOW MANY SEATS ARE THERE IN EACH ROW?

Step 1. Let n be the number of rows.

Step 2. Let n+5 be the number of seats per row.

Step 3. Then, n(n+5)=150 since there are 150 seats.

Step 4. Subtract 150 to both sides of equation in Step 3.





Step 5. To solve, use the quadratic equation given as



where a=1, b=5, and c=-150

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=625 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 10, -15. Here's your graph:

Selecting the positive solution of and and note the product is 150 seats.

Step 6. ANSWER: The number of seats in each row is 15 seats.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Dr J
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You can put this solution on YOUR website!
Five years ago, Jhons age was half of the age he will be in 8 years. How old is he now?

Step 1. Let x be the age of Jhons.

Step 2. Let x-5 be the age of Jhons five years ago.

Step 3. Let x+8 be the age of Jhons 8 years from now.

Step 4. Then since five years ago, Jhons age was half of the age he will be in 8 years

Step 5. Solving the equation in Step 4 yields the following steps

Multiply by 2 to get rid of the denominator





Add 10-x to both sides of the equation





Check equation in Step 4 or . Then which is a true statement.

Step 6. ANSWER: The age of Jhons is 18 years old.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Dr J

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By looking at two linear equations, is there a way you can you tell if the corresponding lines are parallel?

Step 1. Two lines are parallel when they have the same slope, say m.

Step 2. So the two linear equations should be in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).

Step 3. Example: y=2x+3 and y=2x-9. These two line are parallel since the slope is m=2.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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What is the LCM of 5(x-3) and 15(x-3).

Step 1. The Least Common Multiple is the smallest number that is a multiple of two or more numbers.

Step 2. In this example, looking first at the numbers, the Least Common Multiple of 5 and 15 is 15, because 15 is a multiple of 15 and also a multiple of 5.

Step 3. Also x-3 is the least common multiple between the two terms.

Step 4. ANSWER: The LCM is 15(x-3).

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm.

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 2w+3 be the length since the length is three cm longer than twice the width.

Step 4. Then, P=w+w+2w+3+2w+3=90.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: w=14. Graphical form: Equation was fully solved. Text form: w+w+2w+3+2w+3=90 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( w+w+2w+3+2w+3=90 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Added fractions or integers together It becomes . Look at . Moved to the right of expression It becomes . Look at . Eliminated similar terms ,,, replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Moved these terms to the left It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Solved linear equation equivalent to 6*w-84 =0 It becomes . Result: This is an equation! Solutions: w=14. Universal Simplifier and Solver Done!

For w=14 , then 2w+3=31 and P=2(14+31)=90 which is a true statement.

Step 6. ANSWER: The width is 14 cm and the length is 31 cm.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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http://www.Twitter.com/FreedomUTVep 1. Let w be the width

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The perimeter of a rectangle is 70 m. The length is 8 meters more than twice the width. Find the length and width.

Step 1. The perimeter P means adding up all the four sides of a rectangle.

Step 2. Let w be the width.

Step 3. Let 2w+8 be the length since the length is 8 meters more than twice the width

Step 4. Then, P=w+w+2w+8+2w+8=70.

Step 5. Solving yields the following steps

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: w=9. Graphical form: Equation was fully solved. Text form: w+w+2w+8+2w+8=70 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( w+w+2w+8+2w+8=70 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Added fractions or integers together It becomes . Look at . Moved to the right of expression It becomes . Look at . Eliminated similar terms ,,, replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Moved these terms to the left It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Solved linear equation equivalent to 6*w-54 =0 It becomes . Result: This is an equation! Solutions: w=9. Universal Simplifier and Solver Done!

For w=9 , then 2w+8=26 and P=2(9+26)=70 which is a true statement.

Step 6. ANSWER: The width is 9 meters and length is 26 meters.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

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Dr J
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Can you help me solve this equation by substitution?

8x+2y=6
4x=3-y or 4x+y=3

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve: We'll use substitution. After moving 2*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV

Rectangles/227743: Find an algebraic expression. The perimeter of a rectangle, given that the length is x yards and the width is 10 yards shorter. 1 solutions Answer 169213 by drj(1380)   on 2009-10-16 22:10:24 (Show Source): You can put this solution on YOUR website! Find an algebraic expression. The perimeter of a rectangle, given that the length is x yards and the width is 10 yards shorter. Step 1. Perimeter P means adding up all four sides of the rectangle. Step 2. x-10 be the width of the rectangle since the width is 10 yards shorter. Step 3. P=x+x+x-10+x-10=4x-20 Step 4. ANSWER: Perimeter P=4x-20 (in yards). I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV

Rate-of-work-word-problems/227749: A picture 8 inches long and 6 inches wide is to be enlarged so that its length will be 12 inches. What is the width in inches, of the enlarged picture? a.6 b. 3 c. 2 4. 8 5.9 1 solutions Answer 169212 by drj(1380)   on 2009-10-16 22:06:38 (Show Source): You can put this solution on YOUR website! A picture 8 inches long and 6 inches wide is to be enlarged so that its length will be 12 inches. What is the width in inches, of the enlarged picture? a.6 b. 3 c. 2 4. 8 5.9 Step 1. Assume the same proportions such that where w is the width of the enlarged picture Step 2. Solving Multiply by 3w/4 to both sides of the equation Step 3. ANSWER: The enlarged width is 9 inches. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV

Travel_Word_Problems/227740: if a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip? 1 solutions Answer 169210 by drj(1380)   on 2009-10-16 22:00:18 (Show Source): You can put this solution on YOUR website! If a car averages 55 mph on a certain trip, it will arrive 2 hours early. If the car averages 35 mph it will arrive 2 hours late. How many miles is the trip? Step 1. distance = speed * time Step 2. Let t be the time of the trip traveling on time. Step 3. Let t-2 be the time if traveling at 55 mph. Step 4. Let 55(t-2) be the distance traveling at 55 mph. Step 5. Let 35(t+2) be the distance traveling at 35 mph. Step 6. Then, 55(t-2)=35(t+2) since the distances are equal in Steps 4 and 5. Step 7. Solving the equation in Step 6 yields the following steps Add 110-35t to both sides of the equation Divide by 20 to both sides of the equation Substitute the value of t in Steps 4 or 5. We'll do both to check if distances are equal miles and miles. Step 8. The distance is 385 miles. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV

Linear_Equations_And_Systems_Word_Problems/227736: I need help solving this equation: 1 solutions Answer 169204 by drj(1380)   on 2009-10-16 21:46:19 (Show Source): You can put this solution on YOUR website! I need help solving this equation: Step 1. Add to both sides of the equation. where we simplified and arranged in descending order. Step 2. To solve, use the quadratic equation given as where a=1, b=9 and c=18. Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=9 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -3, -6. Here's your graph: Step 3. ANSWER: The solutions are -3 and -6. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV

Equations/227738: Can you help me solve the system? x+2y=-12 y=20-2x 1 solutions Answer 169200 by drj(1380)   on 2009-10-16 21:42:09 (Show Source): You can put this solution on YOUR website! Can you help me solve the system? x+2y=-12 y=20-2x or 2x+y=20 Solved by pluggable solver: SOLVE linear system by SUBSTITUTION Solve: We'll use substitution. After moving 2*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Equations/227739: I need help solving this equation Solve the system 2x+5y=1 -x+6y=8 1 solutions Answer 169198 by drj(1380)   on 2009-10-16 21:40:16 (Show Source): You can put this solution on YOUR website! I need help solving this equation Solve the system 2x+5y=1 -x+6y=8 Solved by pluggable solver: SOLVE linear system by SUBSTITUTION Solve: We'll use substitution. After moving 5*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Equations/227730: Can someone pls show me how to solve this equation using the addition/elimination process? 1.8x-2y=0.9 0.04x+0.18y=0.15 1 solutions Answer 169197 by drj(1380)   on 2009-10-16 21:29:13 (Show Source): You can put this solution on YOUR website! Can someone pls show me how to solve this equation using the addition/elimination process? 1.8x-2y=0.9 Equation A 0.04x+0.18y=0.15 Equation B Step 1. Multiply by 0.09 to Equation A to both sides of the equation Equation A1 Equation B Step 2. Add Equations A1 and B to eliminate the y terms. Step 3. Divide by 0.202 to both sides of the equation Step 4. Substitute into Equation A to solve for y. Step 5. Add 2y-0.9 to both sides of the equation Step 6. Divide by 2 to both sides of the equation Step 7. ANSWER: The solution is and As a check, use the substitution shown below which have the same results. Solved by pluggable solver: SOLVE linear system by SUBSTITUTION Solve: We'll use substitution. After moving -2*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Coordinate-system/227726: When traveling to work each day, John drives part of it on the highway (where he goes 65 mph) and the rest on a ranch road (where he can only go 42 mph). The trip is 13.95 miles, and it takes only 15 minutes (which is 1/4 hour , or 0.25 hours). What part of an hour does he spend driving on each type of road? 1 solutions Answer 169196 by drj(1380)   on 2009-10-16 21:14:55 (Show Source): You can put this solution on YOUR website! When traveling to work each day, John drives part of it on the highway (where he goes 65 mph) and the rest on a ranch road (where he can only go 42 mph). The trip is 13.95 miles, and it takes only 15 minutes (which is 1/4 hour , or 0.25 hours). What part of an hour does he spend driving on each type of road? Step 1. Let t be the time (in hours) traveled on the highway. Step 2. Let 65t be the distance traveled on the highway. Step 3. Let 0.25-t be the time traveled (in hours) on the ranch road. Step 4. Let 42(.25-t) be the distance traveled on the ranch road. Step 5. Then 13.95=65t+42(0.25-t)=10.5+23t since the total distance is 13.95 miles. Step 6. Solving yields the following steps Subtract 10.5 from both sides of the equation Divide by 23 to both sides of the equation hour and hour Check distance traveled 65*0.15+42*0.10=9.75+4.2=13.95 which is a true statement. Step 7. ANSWER: John spent 0.15 hour on the highway and 0.10 hour on the ranch road. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Linear-equations/227722: 7x+7y=28 -7x+y=57 Solve by the substitution method 1 solutions Answer 169195 by drj(1380)   on 2009-10-16 20:59:11 (Show Source): You can put this solution on YOUR website! 7x+7y=28 -7x+y=57 Solve by the substitution method Solved by pluggable solver: SOLVE linear system by SUBSTITUTION Solve: We'll use substitution. After moving 7*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Travel_Word_Problems/227725: An airplane flew with the wind for 5 hours. The return trip against the wind took 6 hours. If the wind was blowing at 25mph. What was the rate of the plane in still the air? 1 solutions Answer 169194 by drj(1380)   on 2009-10-16 20:56:54 (Show Source): You can put this solution on YOUR website! An airplane flew with the wind for 5 hours. The return trip against the wind took 6 hours. If the wind was blowing at 25mph. What was the rate of the plane in still the air? Step 1. distance= speed * time Step 2. Let x+25 be the airplane speed with the wind. Step 3. Let x-25 be the airplane speed against the wind. Step 4. Let 5(x+25) be the distance traveled with the wind after 5 hours. Step 5. Let 6(x-25) be the distance traveled again the wind after 6 hours. Step 6. Equate Steps 4 and 5 since the distances are the same. Add 150-5x to both sides of the equation Check if distances are equal: (275+25)5=(275-25)6 which is a true statement. Step 7. ANSWER: The speed of the plane is 275 miles per hour. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Travel_Word_Problems/227721: The speed of train A is 12 km/hr is slower than the speed of train B. Train A travels 230 km in the same time it takes train B to travel 290 km,. Find the speed of each. 1 solutions Answer 169192 by drj(1380)   on 2009-10-16 20:48:35 (Show Source): You can put this solution on YOUR website! The speed of train A is 12 km/hr is slower than the speed of train B. Train A travels 230 km in the same time it takes train B to travel 290 km,. Find the speed of each. Step 1. or Step 2. Let x be the speed of train B Step 3. Let x-12 be the speed of train A since it is 12 km/hr slower. Step 4. Let be the time traveled by train A. Step 5. Let be the time traveled by train B. Step 6. Set the equations in Steps 4 and 6 since they traveled at the same time. Multiply by to both sides of the equation to get rid of the denominators. Add 3480-230x to both sides of the equation Divide by 60 to both sides of the equation speed of Train B and hours which is a true statement. Step 7. ANSWER: The speed of Train A is 46 km/hr and speed of Train B is 58 km/hr. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Linear-systems/227550: Why is it true that at x-intercept, the value of y is 0, and at y-intercept, the value of x is 0? 1 solutions Answer 169183 by drj(1380)   on 2009-10-16 19:59:49 (Show Source): You can put this solution on YOUR website! Why is it true that at x-intercept, the value of y is 0, and at y-intercept, the value of x is 0? To answer your question, let's look at an example shown below by graphing two points since two points make a line: Equation of a line in standard form. Step 1. Let x=0 then 5y=10 or y=2. So one point is (0,2). Step 2. Let y=0 then 2x=10 or x=5. So another point is (5,0). Step 3. Now, draw a graph using these two points (0,2) and (5,0). Step 4. Note that at point (0,2) the line intersects the y-axis and at point(5,0) the line intersects the x-axis. So the y-intercept is when x=0 or at point (0,2). And the x-intercept is when y=0 or at point (5,0). I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Linear_Equations_And_Systems_Word_Problems/227712: eight times a number plus six less than twice the number is 34 1 solutions Answer 169180 by drj(1380)   on 2009-10-16 19:50:34 (Show Source): You can put this solution on YOUR website! Eight times a number plus six less than twice the number is 34. Step 1. Let n be the number. Step 2. Let 8n be eight times a number Step 3. Let 8n+2n-6 be eight times a number plus 6 less than twice the number Step 4. Then 8n+2n-6=34 since eight times a number plus six less than twice the number is 34. Step 5. Solving yields the following steps. Add 6 to both sides of the equation Divide by 10 to both sides of the equation Step 6. ANSWER: The number is 4. I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Trigonometry-basics/227714: -6-4y=-24 2x+7y=13 1 solutions Answer 169176 by drj(1380)   on 2009-10-16 19:34:57 (Show Source): You can put this solution on YOUR website! -6-4y=-24 Equation A (see Step 8 if you meant -6x-4y=-24) 2x+7y=13 Equation B Step 1. Solve for y in Equation A . Step 2. Add 6 to both sides of the equation Step 3. Divide by -4 to both sides of the equation Step 4. Now substitute into . Step 5. Subtract from both sides of the equation Step 6. Divide by 2 to both sides of the equation Step 7. ANSWER: and Step 8. Now, I'll assume you meant to solve the following linear system of equations -6x-4y=-24 Equation A 2x+7y=13 Equation B Solved by pluggable solver: SOLVE linear system by SUBSTITUTION Solve: We'll use substitution. After moving -4*y to the right, we get: , or . Substitute that into another equation: and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. error_location: 101 I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Equations/227711: How would you write the line x=4 in standard form ? 1 solutions Answer 169169 by drj(1380)   on 2009-10-16 19:20:16 (Show Source): You can put this solution on YOUR website! How would you write the line x=4 in standard form ? Step 1. The given equation is already in standard form. Step 2. The standard form is given as Ax+By=C where A, B, and C are constants. Step 3. Then, for then A=1, B=0, and C=4. Step 4. ANSWER: So in standard form we have or simplifying I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV Travel_Word_Problems/227708: Two vehicles, a car and a truck. leave an intersection at the same time. The car heads east at an average speed of 60 miles per hour, while the truck heads south at an average speed of 20 miles per hour. Find an expression for their distance apart d in miles at the end of t hours. 1 solutions Answer 169163 by drj(1380)   on 2009-10-16 19:05:19 (Show Source): You can put this solution on YOUR website! Two vehicles, a car and a truck. leave an intersection at the same time. The car heads east at an average speed of 60 miles per hour, while the truck heads south at an average speed of 20 miles per hour. Find an expression for their distance apart d in miles at the end of t hours. Step 1. distance= speed * time. Step 2. Let 60t be the car traveling EAST at 60 miles per hour after t hours Step 3. Let 20t be the distance of the truck traveling SOUTH at 20 miles per hour after t hours. Step 4. Use the Pythagorean Theorem to find the distance d (hypotenuse) given as the sum of the squares of the legs (legs for our example given as 60t and 20t) is equal to the square of the hypotenuse d. Take the square root to both sides of the equation yields Step 5. ANSWER is I hope the above steps were helpful. For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry. And good luck in your studies! Respectfully, Dr J http://www.FreedomUniversity.TV