# How do you solve abs(8 - 3x) = 11?

Jul 3, 2015

The answer is $x = - 1$ or $x = \frac{19}{3}$.

#### Explanation:

First of all we must remember the definition of the absolute value, which is done by cases:
If $x > 0 \implies \left\mid x \right\mid = x$
If $x < 0 \implies \left\mid x \right\mid = - x$
Applying this to our question, we obtain the following:
If $\left(8 - 3 x\right) > 0 \implies \left\mid 8 - 3 x \right\mid = 8 - 3 x$
Then, $\left\mid 8 - 3 x \right\mid = 11 \implies 8 - 3 x = 11 \implies - 3 x = 3 \implies x = - 1$
If $\left(8 - 3 x\right) < 0 \implies \left\mid 8 - 3 x \right\mid = - \left(8 - 3 x\right) = 3 x - 8$
Then, $\left\mid 8 - 3 x \right\mid = 11 \implies 3 x - 8 = 11 \implies 3 x = 19 \implies x = \frac{19}{3}$