# How do you solve abs(3x+2)=14?

Jul 16, 2015

$\textcolor{red}{x = 4}$ and $\textcolor{red}{x = - \frac{16}{3}}$.

#### Explanation:

We need to write two different equations without the absolute value symbols and solve for $x$.

These equations would be

(1): $\left(3 x + 2\right) = 14$
(2): $- \left(3 x + 2\right) = 14$

Solve Equation 1:

$3 x + 2 = 14$

Subtract $2$ from each side.

$3 x = 12$

Divide each side by $3$.

$x = 4$

Solve Equation 2.

−(3x+2) = 14

Remove parentheses.

−3x−2= 14

Add $2$ to each side.

$- 3 x = 16$

Divide each side by $- 3$.

$x = - \frac{16}{3}$

The solutions are $x = 4$ and $x = - \frac{16}{3}$.

Check:

If $x = 4$,

$| 3 x + 2 | = 14$
|3×4 +2|= 14
$| 12 + 2 | = 14$
$| 14 | = 14$
$14 = 14$

If $x = - \frac{16}{3}$,

$| 3 x + 2 | = 14$
|3×(-16/3) + 2| = 14
$| - 16 + 2 | = 14$
$| - 14 | = 14$
$14 = 14$