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If Kevin is 5 years older than Bob and in 3 years time he will be twice his age.
How old is Kevin and Bob now?

Step 1. Let x be the age of Bob.

Step 2. Let x+5 be the age of Kevin since he's 5 years older than Bob

Step 3. Let x+3 be the age of Bob in 3 years.

Step 4. Let x+5+3=x+8 be the age of Kevin in three years.

Step 5. Then, x+8=2(x+3) since in three years time Kevin will be twice Bob's age.

Step 6. Solving the equation in Step 5 leads to the following steps



Subtract 6+x from both sides of the equation





and . In three years 7+3=2(2+3) or 10=10 as a check in three years time Kevin is twice as old as Bob.

Step 7. ANSWER: The age of Bob is 2 and the age of Kevin is 7.


I hope the above steps were helpful.

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The second of two numbers is 4 times the first. Their sum is 50. Find the number.

Step 1. Let x be the first number.

Step 2. Let 4x be the second number since it is 4 times the first.

Step 3. Let x+4x=50 be the sum of the two numbers and is given as 50.

Step 4. Solving the equation in Step 3 leads to the following steps.



Divide by 5 to both sides of the equation to get x



and . Also, the sum of 10 and 40 is 50 as a check of the solution.

Step 5. ANSWER: The numbers are 10 and 40.


I hope the above steps were helpful.

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Step 1. Subtract x from both sides of the equation





Step 2. Check solution with original equation



which is a true statement

Step 3. ANSWER: The solution is


I hope the above steps were helpful.

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The sum of four consecutive odd integers is 216 . Find the four integers

Step 1. Let n be the first odd integer.

Step 2. Let n+2, n+4, and n+6 be the next three consecutive odd integers

Step 3. Then, n+n+2+n+4+n+6=216 since the sum of the four consecutive odd integers is 216.

Step 4. Solving the equation in Step 4 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: n=51. Graphical form: Equation was fully solved. Text form: n+n+2+n+4+n+6=216 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( n+n+2+n+4+n+6=216 ) 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 4*n-204 =0 It becomes . Result: This is an equation! Solutions: n=51. Universal Simplifier and Solver Done!

With n=51, then n+2=53, n+4=55, and n+6=57. Also 51+53+55+57=216 as a check...

Step 5. The four consecutive odd integers are 51, 53, 55, and 57


I hope the above steps were helpful.

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Set up a system of two equations with two variables to solve this problem. The three angles in a triangle always add up to 180 degrees. If one angle in a triangle is 132 degrees and the second is 5 times the third, what are the three angles?

Step 1. Let x be the third angle.

Step 2. Let y=5x since the second is 5 times the third.

Step 3. Let x+y+132=180 since all three angles add up to 180 degrees. We can rewrite this after subtracting 132 from both side of the equation as





Step 4. The system of equations are





Step 5. Substitute into to get }. Then



Divide by 6 to both sides of the equation



and . Also 132+8+40=180...as a check.

Step 6. ANSWER: The angles are 132, 8, and 40 degrees.


I hope the above steps were helpful.

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The perimeter of a rectangle is 126 cm. The rectangle is twice as long as it is wide. What are its dimensions?

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 be the length

Step 4. Then, P=w+w+2w+2w=126.

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=21. Graphical form: Equation was fully solved. Text form: w+w+2w+2w=126 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( w+w+2w+2w=126 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION 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 . Solved linear equation equivalent to 6*w-126 =0 It becomes . Result: This is an equation! Solutions: w=21. Universal Simplifier and Solver Done!

For w=21 , then 2w=42 and P=2(21+42)=126 which is a true statement.

Step 6. ANSWER: The width is 21 cm and the length is 42 cm.

I hope the above steps were helpful.

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Find the y- and x-intercepts for the equation.
4) f(x) = - 3 - 7x

Step 1. Given y=f(x)=-3-7x, then x-intercepts occur when y=0. Then 0=-3-7x leads to
Adding 7x to both sides of the equation





Divide by 7 to both sides of the equation





Step 2. Given y=-3x-7, y-intercepts occur when x=0, y=-3*x-7 or y=-7.

Step 3. ANSWER: The x-intercept occurs at point (-3/7,0) and the y-intercept occurs at point(0,-7).

I hope the above steps were helpful.

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The sum of three consecutive integers is -129. Find the integers.

Step 1. Let n be the first integer.

Step 2. Let n+1 and n+2 be the next two consecutive integers.

Step 3. Then, n+n+1+n+2=-129 since the sum is -129.

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result: YOUR ANSWER Here's what you tried: This is an equation! Solutions: n=-44. Graphical form: Equation was fully solved. Text form: n+n+1+n+2=-129 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( n+n+1+n+2=-129 ) 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 . Solved linear equation equivalent to 3*n+132 =0 It becomes . Result: This is an equation! Solutions: n=-44. Universal Simplifier and Solver Done!

With n=-44, n+1=-43, and n+2=-42. Not the sum of these integers is -129.

Step 4. The integers are -44, -43, and -42.

I hope the above steps were helpful.

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Mary is 3 years older than her brother Tom, and Tom is 4 years older than John. Three years ago Mary was twice as old as John. How old is each now?

Step 1. Let x be the age of John.

Step 2. Let x+4 be the age of Tom since Tom is 4 years older than John

Step 3. Let x+4+3=x+7 be the age of Mary since she is 3 years old than Tom

Step 4. Let x+4+3-3=x+4 be the age of Mary three years ago

Step 5. Let x-3 be the age of John three years ago.

Step 6. Then, x+4=2(x-3) since three years ago Mary was twice as old as John

Step 7. Solving equation in Step 6 yields the following steps



Add 6-x to both sides to get numbers only on one side and the variable x on the other side.



John's age

Then Tom's age and Mary's age.

Check...if equation in Step 6 is true. Three years ago Mary was 14 years old which is twice the age of John who was 7 years old which satisfies Step 6.

Step 8. ANSWER: John is 10 years old, Tom is 14 years old and Mary is 17 years old.

I hope the above steps were helpful.

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Find two consecutive even integers whose sum is 117.

Step 1. Let n be the first even integer.

Step 2. Let n+2 be the next consecutive even integer.

Step 3. Then n+n+2=117 since two consecutive even integers whose sum is 117.

Step 4. Solving yields the following steps.



Divide by 2 to both sides of the equation



but this is not an even integer.

Step 5. ANSWER: There is no solution to this problem. Note the addition of two even integers will not yield an odd integer.

I hope the above steps and explanation were helpful.

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Graph the line that passes through the point(-1,2)and has slope –4/3.

Step 1. Starting with the (-1,2) or x=-1 and y=2, we move units to the RIGHT and units DOWN since the slope . This means we have another point at (-1+3,2-4) or (2, -2).

Step 3. Use the two points (-1,2) and (2,-2) to plot the line.



I hope the above steps were helpful.

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Graph where m is the slope and b is the y-intercept when x=0 or at point (0,b). In this case, and or y-intercept at (0,-3)

Step 2. Starting with the y-intercept at (0,-3) or x=0 and y=-3, we move two units to the right and one unit up since the slope is 1/2. This means we have another point at (0+2,-3+1) or (2, -2).

Step 3. Use the two points (0,-3) and (2,-2) to plot the line.



I hope the above steps were helpful.

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How do you solve this one?

Step 1. Add 4 to both sides of the equation





Step 2. Divide 6 to both sides of the equation





Step 3. Check solution with original equation





which is a true statement

Step 4. ANSWER: Solution is

I hope the above steps were helpful.

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Step 1. I assume you want to plot this linear equation given in standard form.

Step 2. It takes two point to generate a line.

Step 3. Let x=0 then



Divide 4 to both sides of the equation

. So one point is (0,15/4).

Step 4. Let y=0, then



Divide 2 to both sides of the equation

. So another point is (15/2, 0).

Step 5. Use these two points (0,15/4) and (15/2,0) to plot the line.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 15/2 = 7.5. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 15/4 = 3.75. Slope is -2/4 = -0.5. Equation in slope-intercept form: y=-0.5*x+3.75.

I hope the above steps were helpful.

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Use algebra so solve (x-1)(x+2)=18

Step 1. Multiply out to get rid of the parenthesis.





Step 2. Subtract 18 from both sides of the equation





and or and

Step 4. We can also solve using the quadratic equation shown below:



where a=1, b=1 and c=-20

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=81 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, -5. Here's your graph:

...same as before.

Step 5. ANSWER: The solutions are x=-5 and x=4.

I hope the above steps were helpful.

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The sum of two numbers is 42. If the larger number is 3 more than triple the number find both numbers

Step 1. Let x be the larger number.

Step 2. Let 42-x be the other and smaller number.

Step 3. Then, x=3+3(42-x) where I assume you meant the larger number is 3 more than triple the smaller number.

Step 4. Solving the equation in Step 3 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: x=32.25. Graphical form: Equation was fully solved. Text form: x=3+3*(42-x) simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( x=3+3*(42-x) ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved to the right of expression It becomes . Look at . Moved to the right of expression It becomes . Look at . Moved these terms to the left , It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of 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 . Solved linear equation equivalent to 4*x-129 =0 It becomes . Result: This is an equation! Solutions: x=32.25. Universal Simplifier and Solver Done!

Let x=32.25, then 42-32.25=9.75. Check if equation is satisfied in Step 3.

32.25=3+3*9.75 which is a true statement.

I hope the above steps were helpful.

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For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?

What is the answer?

Step 1. Let be the first odd integer.

Step 2. Let and and be the next two consecutive integers.

Step 3. Let since the sum of the least and greatest is 146.

Step 4. Solving the equation in Step 3 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: n=71. Graphical form: Equation was fully solved. Text form: n+n+4=146 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( n+n+4=146 ) If you have a website, here's a link to this solution. DETAILED EXPLANATION 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 2*n-142 =0 It becomes . Result: This is an equation! Solutions: n=71. Universal Simplifier and Solver Done!

With n=71, then n+2=73 and n+4=75 where the sum of the least and largest number is 146. The sum is 71+73+75=219

Step 8. ANSWER: The sum of the numbers is 219.

I hope the above steps were helpful.

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The shorter leg of a right triangle is 20 yards. If the hypotenuse is 29 yards, how long is the other leg?

Step 1. Use the Pythagorean Theorem which states that the sum of the squares of the legs (given legs a and) is equal to the square of the hypotenuse c.



Step 2. Let a=20 and c=29, we can find the other leg b as follows



Subtract from both sides of the equation





Take the square root of b to both sides of the equation



Step 3. ANSWER. The length of the other leg is 21 yards.

I hope the above steps were helpful.

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The difference between two numbers is 22. If the larger number is 4 more than twice the smaller. Find the numbers

Step 1. Let x be one number

Step 2. Let 22+x be the larger number and since the difference between the two numbers is 22.

Step 3. Let 2x be twice the smaller.

Step 4. 22+x=4+2x since the larger number is 4 more than twice the smaller.

Step 5. Solving the equation in Step 4 leads to 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: x=18. Graphical form: Equation was fully solved. Text form: 22+x=4+2x simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( 22+x=4+2x ) If you have a website, here's a link to this solution. DETAILED EXPLANATION Look at . Moved to the right of expression It becomes . Look at . Moved to the right of expression It becomes . Look at . Moved these terms to the left , It becomes . 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 . Removed extra sign in front of It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Remove extraneous '1' from product It becomes . Look at . Solved linear equation equivalent to -x+18 =0 It becomes . Result: This is an equation! Solutions: x=18. Universal Simplifier and Solver Done!

With x=18, then 22+x=40

Check with equation four 22+x=4+2x or 40=4+2*18 or 40=40 which is a true statement.

Step 6. Then numbers are 18 and 40


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Step 1. Subtract 1 from both sides of the equation





Step 2. Divide by -4 to both sides of the equation





Step 3. ANSWER: The solution is

I hope the above steps were helpful.

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THE PERIMETER IS 1280, THE WIDTH IS 90 LESS THAN THE LENGTH, WHAT IS 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 w+90 be the length since the width is 90 less than the length

Step 4. Then, P=w+w+w+90+w+90=1280.

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=275. Graphical form: Equation was fully solved. Text form: w+w+w+90+w+90=1280 simplifies to 0=0 Cartoon (animation) form: For tutors: simplify_cartoon( w+w+w+90+w+90=1280 ) 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 4*w-1100 =0 It becomes . Result: This is an equation! Solutions: w=275. Universal Simplifier and Solver Done!

For w=275 , then w+90=365 and P=2(275+365)=1280 which is a true statement.

Step 6. ANSWER: The length is 365 and the width is 275

I hope the above steps were helpful.

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Solve by method of elimination:

2x +3y =10 Equation A
-3x+y =18 Equation B

Step 1. Multiply Equation B by 3 and subtract from Equation A to eliminate y terms







Step 2. Divide by 11 to both sides of the equation





Step 3. Substitute in Equation A to find y





Step 4. Add 8 to both sides of the equation to find y





Step 5. Divide by 3 to both sides of the equation





Step 6. Check solution of and with Equation B





which is a true statement.

Step 7. ANSWER: The solution is (-4,6) or x=-4 and y=6 for the linear system of equations.

I hope the above steps and explanation were helpful.

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Find the area of a rectangle with base of 2yd and height 5ft

Step 1. Area A=b*h where b is the base and h is the height

Step 2. 1 yard = 3 feet or 2 yards = 6 feet.

Step 3. A=6*5=30 square feet

Step 4. ANSWER: The area is 30 square feet.

I hope the above steps and explanation were helpful.

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Step 1. Let , then .

Step 2. Then,



Step 3. To solve equation in Step 2, use the quadratic formula



where a=1, b=6, and c=-27

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=144 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3, -9. Here's your graph:

With and or and

So , , and where

Step 4. ANSWER: So , , and

I hope the above steps and explanation 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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Respectfully,
Dr J
http://www.FreedomUniversity.TV

You can put this solution on YOUR website!
Perimeter of a rectangle. The perimeter of a rectangular backyard is 6x + 6 yards. If the width is x yards, find a binomial that represents the length.

Step 1. Perimeter P means adding up all the sides of the rectangles.

Step 2. Let L be the length and x be the width.

Step 3. Then P=x+x+L+L=2x+2L

Step 4. But P=6x+6=2x+2L. Solving for L yields the following steps:

Subtract 2x from both sides of the equation







Step 5. ANSWER. The length of the rectangle is

I hope the above steps and explanation 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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Respectfully,
Dr J
http://www.FreedomUniversity.TV

You can put this solution on YOUR website!
Find the equation of the line containing the point (8, –39) and parallel to the line 6x+y= -4 .

Step 1. We can find the slope by recognizing that parallel lines have the same slope. So we need to put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept b when x=0 or at point (0,b).
We can transform the given equation by subtracting -6x from both sides of the equation



Since is in slope-intercept form given as y=mx+b where the slope m=-6 and the y-intercept b=-4 when x=0 or at point (0,b) or (0,-4).

Step 2. Now we have to find the line with slope m=-6 going through point (8,-39).

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as



Step 4. Let (x1,y1)=(8,-39) or x1=8 and y1=-39. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:





Step 6. Multiply x-8 to both sides to get rid of denominator on right side of equation.





Subtract 39 from both sides of the equation





Step 7. ANSWER: The equation in slope-intercept form is


Note: the above equation can be rewritten as



And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 9/6 = 1.5. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 9/1 = 9. Slope is -6/1 = -6. Equation in slope-intercept form: y=-6*x+9.

I hope the above steps and explanation 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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Respectfully,
Dr J
http://www.FreedomUniversity.TV

You can put this solution on YOUR website!
Point (1, –2) , m = –5.

I assume you want to write the slope intercept form of the equation of the line through the given point (1,-2) with the given slope m=-5.

Step 1. The slope-intercept form is 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 2. Now we have to find the line with slope m=-5 going through point (1,-2).

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as



Step 4. Let (x1,y1)=(1,-2) or x1=1 and y1=-2. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:





Step 6. Multiply x-1 to both sides to get rid of denominator on right side of equation.





Step 7. Add -2 to both sides of the equation





Step 7. ANSWER: The equation in slope-intercept form is where the slope m=7 and the y-intercept b=-5.

Note: the above equation can be rewritten in standard form as



And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 3/5 = 0.6. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 3/1 = 3. Slope is -5/1 = -5. Equation in slope-intercept form: y=-5*x+3.

I hope the above steps and explanation 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

You can put this solution on YOUR website!
Write in standard form the equation of the line with slope =-2 and passing through (4,1)

Step 1. The slope-intercept form is given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b). Using the slope-intercept, we can translate it to the standard form given as Ax+By=C where A, B, and C are constants.

Step 2. Now we have to find the line with slope m=-2 going through point (4,1).

Step 3. Given two points (x1,y1) and (x2,y2), then the slope m is given as



Step 4. Let (x1,y1)=(4,1) or x1=4 and y1=1. Let other point be (x2,y2)=(x,y) or x2=x and y2=y.

Step 5. Now we're given . Substituting above values and variables in the slope equation m yields the following steps:





Step 6. Multiply x-4 to both sides to get rid of denominator on right side of equation.





Step 7. Add 1 to both sides of the equation





Step 7. ANSWER: The equation in slope-intercept form is where the slope m=-2 and the y-intercept b=9. The above equation can be rewritten in standard form by adding 2x to both sides as .

And the graph is shown below which is consistent with the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc

Equation describes a sloping line. For any equation ax+by+c = 0, slope is . X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 9/2 = 4.5. Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 9/1 = 9. Slope is -2/1 = -2. Equation in slope-intercept form: y=-2*x+9.

I hope the above steps and explanation 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

You can put this solution on YOUR website!
Solve by elimination

Equation A
Equation B

Step 1. Subtract Equation B from Equation A to eliminate the y-term







Step 2. Multiply by -1 to both sides to get

Step 3. Substitute x=-5 into Equation A to find y



Add 5 to both sides of the equation to get numbers on one side and variable y on the other side.







Divide by -6 to both sides of the equation





Step 4. Check and is solution to Equation B





which is a true statement.

Step 5. ANSWER: The solution is x=-5 and y=-2 or (-5,-2) which is the intersection between these two lines or system of linear equations.

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.

Good luck in your studies!

Respectfully,
Dr J

You can put this solution on YOUR website!
The product of two positive consecutive numbers is 42. What is the larger number?

Step 1. Let n be the smaller positive number.

Step 2. Let n+1 be the next consecutive and larger positive number.

Step 3. Then n(n+1)=42 since their product is 42.

Step 4. Subtract 42 from both sides of the equation to get a quadratic.



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



where a=1, b=1, and c=-42

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=169 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6, -7. Here's your graph:

Selecting the positive solution n=6, then n+1=7. Also note their product is 42.

Step 6. ANSWER: The larger number is 7.

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

You can put this solution on YOUR website!
Solve:

Step 1. Multiply by (a-7)(a+4) to both sides of the equation to get rid of denominators.







Step 2. Add 4a-40 to both sides of the equation to get numbers on one side and variables on the other side.





Step 3. Divide by 14 to both sides of the equation to get a.








Step 4. Check solution with original equation to see if it leads to a true statement.










which is a true statement.

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