Question

3/4x-5=1/2x+2x-10
solve for x

Answer 1

`x=(20)/(7)`

Explanation:

Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.

`(1)/(2)x+2x-10=(3)/(4)x-5`

Simplify the left side of the equation by combing
`(1)/(2)` and
`x`.

`(x)/(2)+2x-10=(3)/(4)x-5`

To write
`2x` as a fraction with a common denominator, multiply by
`(2)/(2)`.

`(x)/(2)+2x*(2)/(2) -10=(3)/(4)x-5`

Simplify terms by combining
`2x` and
`(2)/(2)`. Combine the numerators over the common denominator.

`(x+2x*2)/(2) -10=(3)/(4)x-5`

Raise x to the power of 1.

`(x^1+2x*2)/(2) -10=(3)/(4)x-5`

Factor
`x` out of
`x^1`.

`(x*1+2x*2)/(2) -10=(3)/(4)x-5`

Factor
`x` out of
`x+2x*2`.

`(x*1+x(2*2))/(2) -10=(3)/(4)x-5`

Factor
`x` out of
`x*1+x(2*2)`

`(x(1+2*2))/(2) -10=(3)/(4)x-5`

Multiply 2 by 2.

`(x(1+4))/(2) -10=(3)/(4)x-5`

Add 1 and 4.

`(5x)/(2) -10=(3)/(4)x-5`

Combine
`(3)/(4)` and
`x`.

`(5x)/(2) -10=(3x)/(4)-5`

Move all terms containing
`x` to the left side of the equation.

`(7x)/(4)-10=-5`

Move all terms not containing
`x` to the right side of the equation.

`(7x)/(4)=5`

Multiply both sides of the equation by
`(4)/(7)`

`(7x)/(4)*(4)/(7) =5*(4)/(7)`

Simplify both sides of the equation.

`x=(20)/(7)`

Answer 2

x =
`(20)/(7)`

Explanation:

`(3)/(4)` x - 5=
`(1)/(2)` x + 2x - 10

multiply through by 4 ( the LCM of 4 and 2 ) to clear the fractions

3x - 20 = 2x + 8x - 40

3x - 20 = 10x - 40 ( subtract 10x from both sides )

- 7x - 20 = - 40 ( add 20 to both sides )

- 7x = - 20 ( divide both sides by - 7 )

x =
`(-20)/(-7)` =
`(20)/(7)`