# How do you solve 3abs(x+7)-14=4?

Jun 12, 2018

$x = - 13 \text{ or } x = - 1$

#### Explanation:

$\text{the expression inside the absolute value can be }$
$\text{positive or negative hence there are 2 possible solutions}$

$\text{add 14 to both sides and divide by 3}$

$| x + 7 | = \frac{18}{3} = 6$

$\textcolor{m a \ge n t a}{\text{positive expression}}$

$x + 7 = 6 \Rightarrow x = - 1$

$\textcolor{m a \ge n t a}{\text{negative expression}}$

$- \left(x + 7\right) = 6$

$- x - 7 = 6 \Rightarrow - x = 6 + 7 = 13 \Rightarrow x = - 13$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into the equation and if the left side equals the right side then they are the solutions.

$x = - 1$

$3 | - 1 + 7 | - 14 = \left(3 \times 6\right) - 14 = 18 - 14 = 4$

$x = - 13$

$3 | | - 6 | - 14 = \left(3 \times 6\right) - 14 = 18 - 14 = 4$

$x = - 1 \text{ or "x=-13" are the solutions}$