Question

How do you solve `|- 3( x - 7) | = 21`?

Answer 1

`x = 0` and `x = 14`

Explanation:

Because `|21| = |-21| = 21`, we can remove the absolute value from the equation as such

`|-3(x-7)| = 21`
`-3(x-7) = +- 21`

We then have two equations (differentiated by the `+-` sign) and we solve each using equation manipulation.

`-3(x-7) = 21`
`21 - 3x = 21`
`3x = 0 -> x = 0`

`-3(x-7) = -21`
`21 - 3x = -21`
`42 = 3x`
`x = 42/3 = 14`

Thus, our two solutions are `x = 0` and `x = 14`.