# How do you solve |2.3 - 5.7x| = 11.4?

Mar 13, 2018

Find the solutions of x that give you $\pm 11.4$ inside the absolute value bars. For that scenario, x=-1.5965 and x=2.4035

#### Explanation:

Because we're dealing with an absolute value, x can have two solutions since:

$\left\mid 11.4 \right\mid = 11.4$ and $\left\mid - 11.4 \right\mid = 11.4$

Therefore, we need to find the following solutions:

$2.3 - 5.7 x = 11.4$
$2.3 - 5.7 x = - 11.4$

The first step for both is to subtract 2.3 from both sides, and the second step is to divide by x's coefficient. This gives you the solution:

$x = \frac{11.4 - 2.3}{- 5.7} \Rightarrow x = - \frac{9.1}{5.7} = - 1.5965$

$x = \frac{- 11.4 - 2.3}{- 5.7} \Rightarrow x = \frac{13.7}{5.7} = 2.4035$