Question

How do you solve `-\frac { 1} { 3} ( 9x + 18) - 2x = - 66`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(-1/3)(9x + 18) - 2x = -66`

`(color(red)(-1/3) xx 9x) + (color(red)(-1/3) xx 18) - 2x = -66`

`(color(red)(-9/3)x) + (color(red)(-18/3)) - 2x = -66`

`-3x + (-6) - 2x = -66`

`-3x - 6 - 2x = -66`

Next, group and combine like terms on the left side of the equation:

`-3x - 2x - 6 = -66`

`(-3 - 2)x - 6 = -66`

`-5x - 6 = -66`

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

`-5x - 6 + color(red)(6) = -66 + color(red)(6)`

`-5x - 0 = -60`

`-5x = -60`

Now, divide each side of the equation by `color(red)(-5)` to solve for `x` while keeping the equation balanced:

`(-5x)/color(red)(-5) = (-60)/color(red)(-5)`

`(color(red)(cancel(color(black)(-5)))x)/cancel(color(red)(-5)) = 12`

`x = 12`