Question

How do you solve `\frac { 1} { 2} ( 4x - 6) = - \frac { 3} { 4} x`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(4)` to eliminate the fractions while keeping the equation balanced:

`color(red)(4) xx 1/2(4x - 6) = color(red)(4) xx -3/4x`

`color(red)(4)/2(4x - 6) = cancel(color(red)(4)) xx -3/color(red)(cancel(color(black)(4)))x`

`2(4x - 6) = -3x`

Next, expand the terms within parenthesis on the left side of the equation by multiplying each term within the parenthesis by `2`:

`(2 xx 4x) - (2 xx 6) = -3x`

`8x - 12 = -3x`

Then add `color(red)(12)` and `color(blue)(3x)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`8x - 12 + color(red)(12) + color(blue)(3x) = -3x + color(red)(12) + color(blue)(3x)`

`8x + color(blue)(3x) - 12 + color(red)(12) = -3x + color(blue)(3x) + color(red)(12)`

`11x - 0 = 0 + 12`

`11x = 12`

Now, divide each side of the equation by `color(red)(11)` to solve for `x` while keeping the equation balanced:

`(11x)/color(red)(11) = 12/color(red)(11)`

`(color(red)(cancel(color(black)(11)))x)/cancel(color(red)(11)) = 12/11`

`x = 12/11`