Question

How do you evaluate `\frac{2x}{3}-\frac{3}{4}=\frac{x}{6}+\frac{21}{4}`?

Answer 1

`x=12`

Explanation:

Given:

`(2x)/3-3/4=x/6+21/4`

All denominators are factors of `12`. Multiply both sides by `12`.

`color(red)cancel(color(black)(12))^4((2x)/color(red)cancel(color(black)(3))^1)-color(red)cancel(color(black)(12))^3(3/color(red)cancel(color(black)(4))^1)=color(red)cancel(color(black)(12))^2(x/color(red)cancel(color(black)(6))^1)+color(red)cancel(color(black)(12))^3(21/color(red)cancel(color(black)(4))^1)`

Simplify.

`4xx2x-9=2x+63`

`8x-9=2x+63`

Add `9` to both sides of the equation.

`8x=2x+63+9`

Simplify.

`8x=2x+72`

Subtract `2x` from both sides.

`8x-2x=72`

Simplify.

`6x=72`

Divide both sides by `6`.

`6x=72/6`

Simplify.

`x=12`