Question

How do you solve `3/4(4x+8)=-12` using the distributive property?

Answer 1

See the entire solution process below:

Explanation:

First, we distribute the `color(red)(3/4)` term across each of the terms within the parenthesis:

`(color(red)(3)/color(red)(4) xx 4x) + (color(red)(3)/color(red)(4) xx 8) = -12`

`(color(red)(3)/cancel(color(red)(4)) xx color(red)(cancel(color(black)(4)))x) + (color(red)(3)/cancel(color(red)(4)) xx color(red)(cancel(color(black)(8)))2) = -12`

`3x + 6 = -12`

Next, subtract `color(red)(6)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`3x + 6 - color(red)(6) = -12 - color(red)(6)`

`3x + 0 = -18`

`3x = -18`

Now, divide each side of the equation by `color(red)(3)` to solve for `x` while keeping the equation balanced:

`(3x)/color(red)(3) = -18/color(red)(3)`

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

`x = -6`