# How do you solve abs(3x+5) =1?

Jun 4, 2016

The solutions are $x = - 2$ and $x = - \frac{4}{3}$

#### Explanation:

The absolute value is defined as

$\left\mid a \right\mid = a \mathmr{if} a \ge 0$ and $\left\mid a \right\mid = - a \mathmr{if} a < 0$

Hence the above equation becomes

$\left\mid 3 x + 5 \right\mid = 1 \implies 3 x + 5 = 1 \mathmr{and} 3 x + 5 = - 1$

Then we have two solutions

$3 x + 5 = 1 \implies 3 x = - 4 \implies x = - \frac{4}{3}$

and

$3 x + 5 = - 1 \implies 3 x = - 6 \implies x = - 2$