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

Jul 16, 2015

$\textcolor{red}{x = 0}$ and $\textcolor{red}{x = - \frac{4}{3}}$.

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

These equations would be

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

Solve Equation 1:

$3 x + 2 = 2$

Subtract $2$ from each side.

$3 x = 0$

Divide each side by $3$.

$x = 0$

Solve Equation 2.

−(3x+2) = 2

Remove parentheses.

−3x−2= 2

Add $2$ to each side.

$- 3 x = 4$

Divide each side by $- 3$.

$x = - \frac{4}{3}$

The solutions are $x = 0$ and $x = - \frac{4}{3}$.

Check:

If $x = 0$,

$| 3 x + 2 | = 2$
|3×0 +2|= 2
$| 0 + 2 | = 2$
$| 2 | = 2$
$2 = 2$

If $x = - \frac{4}{3}$,

$| 3 x + 2 | = 2$
|3×(-4/3) + 2| = 2
$| - 4 + 2 | = 2$
$| - 2 | = 2$
$2 = 2$