# How do you solve 2abs(3x - 4) + 8=6?

Jun 26, 2015

Solve as you would any equation, then make $| 3 x - 4 |$ positive, $3 x - 4 = - 1$, and negative, $- \left(3 x - 4\right) = - 1$. Solve for $x$.

#### Explanation:

$2 | 3 x - 4 | + 8 = 6$

Subtract $8$ from both sides.

$2 | 3 x - 4 | = - 2$

Divide both sides by $2$.

$| 3 x - 4 | = - 1$

The quantity inside the absolute value symbols can be positive or negative: $3 x - 4 = - 1$ and $- \left(3 x - 4\right) = - 1$

When $| 3 x - 4 |$ is positive:

$3 x - 4 = - 1$

Add $4$ to both sides of the equation.

$3 x = 3$

Divide both sides by $3$.

$x = 1$

When $| 3 x - 4 |$ is negative:

$- \left(3 x - 4\right) = - 1$

$- 3 x + 4 = - 1$

Subtract $4$ from both sides.

$- 3 x = - 5$

Divide both sides by $- 3$.

$x = \frac{5}{3}$

Answer: $x = 1 , \frac{5}{3}$