Question

How do you solve `8( x - 2) - 6x = 12`?

Answer 1

See the entire solution process below:

Explanation:

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

`color(red)(8)(x - 2) - 6x = 12`

`(color(red)(8) * x) - (color(red)(8) * 2) - 6x = 12`

`8x - 16 - 6x = 12`

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

`8x - 6x - 16 = 12`

`(8 - 6)x - 16 = 12`

`2x - 16 = 12`

Then, add `color(red)(16)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`2x - 16 + color(red)(16) = 12 + color(red)(16)`

`2x - 0 = 28`

`2x = 28`

Now, divide each side of the equation by `color(red)(2)` to solve for `x` while keeping the equation balanced:

`(2x)/color(red)(2) = 28/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 14`

`x = 14`