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

Apr 12, 2018

$x = 0$ and $x = 14$

#### Explanation:

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

$| - 3 \left(x - 7\right) | = 21$
$- 3 \left(x - 7\right) = \pm 21$

We then have two equations (differentiated by the $\pm$ sign) and we solve each using equation manipulation.

$- 3 \left(x - 7\right) = 21$
$21 - 3 x = 21$
$3 x = 0 \to x = 0$

$- 3 \left(x - 7\right) = - 21$
$21 - 3 x = - 21$
$42 = 3 x$
$x = \frac{42}{3} = 14$

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