# How do you graph and solve 4 |4-3x |= 4x + 6?

Feb 14, 2016

Consider that the absolute value can either be positive or negative. As a result, there will be two solutions.

#### Explanation:

$4 \left(4 - 3 x\right) = 4 x + 6$

$16 - 12 x = 4 x + 6$

$10 = 16 x$

$\frac{5}{8} = x$

Negative scenario:

$4 \left(- \left(4 - 3 x\right)\right) = 4 x + 6$

$4 \left(- 4 + 3 x\right) = 4 x + 6$

$- 16 + 12 x = 4 x + 6$

$- 22 = - 8 x$

$\frac{11}{4} = x$

The solution set is $x = \frac{5}{8} \mathmr{and} \frac{11}{4}$.

Practice exercises:

Solve $2 - | 2 x + 5 | - 4 x = 3 x - 8$