# How do you solve abs(2/3x-9)=18?

May 19, 2017

$x = - \frac{27}{2}$
$x = + \frac{81}{2}$

#### Explanation:

For this to work we have to end up with $| \pm 18 | = + 18$

This means that $\text{ } \frac{2}{3} x - 9 = \pm 18$

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Case 1: $\text{ } \frac{2}{3} x - 9 = + 18$

$\frac{2}{3} x = 27$

Multiply both sides by $\frac{3}{2}$

$x = \frac{3}{2} \times 27 = 40 \frac{1}{2} \to \frac{81}{2}$
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Case 2: $\text{ } \frac{2}{3} x - 9 = - 18$

$\frac{2}{3} x = - 9$

$x = \frac{3}{2} \times \left(- 9\right) = - \frac{27}{2}$