Question

How do you solve `-7( x + 2) = - 23- 4x`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms within parenthesis on the left side of the equation. Multiply each term within the parenthesis by `color(red)(-7)`:

`color(red)(-7)(x + 2) = -23 - 4x`

`(color(red)(-7) xx x) + (color(red)(-7) xx 2) = -23 - 4x`

`-7x - 14 = -23 - 4x`

Next, add `color(red)(7x)` and `color(blue)(23)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`-7x - 14 + color(red)(7x) + color(blue)(23) = -23 - 4x + color(red)(7x) + color(blue)(23)`

`-7x + color(red)(7x) - 14 + color(blue)(23) = -23 + color(blue)(23) - 4x + color(red)(7x)`

`0 + 9 = 0 + 3x`

`9 = 3x`

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

`9/color(red)(3) = (3x)/color(red)(3)`

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

`3 = x`

`x = 3`