Question

How do you solve `-3- 2( 7a - 2) = 9( 3- 3a )`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis on both sides of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`-3 - color(red)(2)(7a - 2) = color(blue)(9)(3 - 3a)`

`-3 - (color(red)(2) xx 7a) + (-color(red)(2) xx -2) = (color(blue)(9) xx 3) - (color(blue)(9) xx 3a)`

`-3 - 14a + 4 = 27 - 27a`

`-3 + 4 - 14a = 27 - 27a`

`1 - 14a = 27 - 27a`

Next, subtract `color(red)(1)` and add `color(blue)(27a)` to each side of the equation to isolate the `a` term while keeping the equation balanced:

`-color(red)(1) + 1 - 14a + color(blue)(27a) = -color(red)(1) + 27 - 27a + color(blue)(27a)`

`0 + (-14 + color(blue)(27))a = 26 - 0`

`13a = 26`

Now, divide each side of the equation by `color(red)(13)` to solve for `a` while keeping the equation balanced:

`(13a)/color(red)(13) = 26/color(red)(13)`

`(color(red)(cancel(color(black)(13)))a)/cancel(color(red)(13)) = 2`

`a = 2`