Questions on Algebra: Evaluation of expressions, parentheses answered by real tutors!

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Question 150558: I’m supposed to solve the below expression for X, but I can’t figure out what I’m doing wrong. I believe your supposed to multiply by the LCD to remove the fraction term. Then when I calculate, I’m completely lost. Maybe I’m using the wrong LCD.

Problem is x+3/6 - x/5 = 9x-5/30
LCD is 30, so I multiplied each term by 30
5(x+3) – 6x = 9x – 5
5x + 15 – 6x = 9x – 5
-x + 15 = 9x – 5
15 = 10x – 5
20 = 10x
x=10
*Answer in my book is x=2

Problem is: 4/x + 2/x+1 = 5
LCD is x(x+1), so I multiplied each term by x(x+1)
4(x+1) + 2x = 5x(x+1)
4x + 4 + 2x = 5x^2 + 5x
6x + 4 = 5x^2 + 5x
4 = 5x^2 + 5x – 6x
4 = 5x^2 – x
*Answer in my book is x=1

Problem is 24/8x - x/3 = 3-x/6
LCD is 24x, so I multiplied each term by 24x
72 – 8 = 4x(3-x)
72 – 8 = 12x – 4x^2
64 = 12x – 4x^2
*Answer in my book is x=3 or x=6

Problem is 6/4(x-2) + 1/4 = 4/x
LCD is 4(x-2), so I multiplied each term by 4(x-2)
6 + x – 2 = x(x-2)
4 + x = x^2 – 2x
4 + x = 0
x = -4
*Answer in my book is x=3 or x=6
: I’m supposed to solve the below expression for X, but I can’t figure out what I’m doing wrong. I believe your supposed to multiply by the LCD to remove the fraction term. Then when I calculate, I’m completely lost. Maybe I’m using the wrong LCD.

Problem is x+3/6 - x/5 = 9x-5/30
LCD is 30, so I multiplied each term by 30
5(x+3) – 6x = 9x – 5
5x + 15 – 6x = 9x – 5
-x + 15 = 9x – 5
15 = 10x – 5
20 = 10x
x=10
*Answer in my book is x=2

Problem is: 4/x + 2/x+1 = 5
LCD is x(x+1), so I multiplied each term by x(x+1)
4(x+1) + 2x = 5x(x+1)
4x + 4 + 2x = 5x^2 + 5x
6x + 4 = 5x^2 + 5x
4 = 5x^2 + 5x – 6x
4 = 5x^2 – x
*Answer in my book is x=1

Problem is 24/8x - x/3 = 3-x/6
LCD is 24x, so I multiplied each term by 24x
72 – 8 = 4x(3-x)
72 – 8 = 12x – 4x^2
64 = 12x – 4x^2
*Answer in my book is x=3 or x=6

Problem is 6/4(x-2) + 1/4 = 4/x
LCD is 4(x-2), so I multiplied each term by 4(x-2)
6 + x – 2 = x(x-2)
4 + x = x^2 – 2x
4 + x = 0
x = -4
*Answer in my book is x=3 or x=6

Answer by jim_thompson5910(9376) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you going in the right direction.

# 1

Good so far until you reach the second to last step

20 = 10x


20/10 = cross(10/10)x Divide both sides by 10.


2 =x Divide 10 into 20 to get 2

So the answer is x=2





# 2

You're off to a good start, I'll start where you left off.

4 = 5x^2 – x Start with the given equation.


0 = 5x^2 – x -4 Subtract 4 from both sides.


Let's use the quadratic formula to solve for x


x = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


x = (-(-1) +- sqrt( (-1)^2-4(5)(-4) ))/(2(5)) Plug in a=5, b=-1, and c=-4


x = (1 +- sqrt( (-1)^2-4(5)(-4) ))/(2(5)) Negate -1 to get 1.


x = (1 +- sqrt( 1-4(5)(-4) ))/(2(5)) Square -1 to get 1.


x = (1 +- sqrt( 1--80 ))/(2(5)) Multiply 4(5)(-4) to get -80


x = (1 +- sqrt( 1+80 ))/(2(5)) Rewrite sqrt(1--80) as sqrt(1+80)


x = (1 +- sqrt( 81 ))/(2(5)) Add 1 to 80 to get 81


x = (1 +- sqrt( 81 ))/(10) Multiply 2 and 5 to get 10.


x = (1 +- 9)/(10) Take the square root of 81 to get 9.


x = (1 + 9)/(10) or x = (1 - 9)/(10) Break up the expression.


x = (10)/(10) or x = (-8)/(10) Combine like terms.


x = 1 or x = -4/5 Simplify.


So the solutions are x = 1 or x = -4/5