# How do you solve -6abs(5-2y) = -9?

Aug 23, 2015

$y = \frac{7}{4} \text{ }$ or $\text{ } y = \frac{13}{4}$

#### Explanation:

Start by isolating the modulus on one side of the equation. This can be done by dividing both sides by $- 6$

(color(red)(cancel(color(black)(-6))) * |5 - 2y|)/color(red)(cancel(color(black)(-6))) = ((-9))/((-6)

$| 5 - 2 y | = \frac{3}{2}$

Since you're dealing with the absolute value of an expression, you must take into account the fact that the expression can be negative or positive.

• $5 - 2 y > 0 \implies | 5 - 2 y | = 5 - 2 y$

$5 - 2 y = \frac{3}{2}$

$2 y = 5 - \frac{3}{2}$

$y = \frac{10 - 3}{2} \cdot \frac{1}{2} = \textcolor{g r e e n}{\frac{7}{4}}$

• $5 - 2 y < 0 \implies | 5 - 2 y | = - \left(5 - 2 y\right)$

This time, the equation becomes

$- \left(5 - 2 y\right) = \frac{3}{2}$

$- 5 + 2 y = \frac{3}{2}$

$2 y = \frac{3 + 10}{2}$

$y = \frac{13}{2} \cdot \frac{1}{2} = \textcolor{g r e e n}{\frac{13}{4}}$

Your original equation has two possible solutions,

$y = \frac{7}{4} \text{ }$ or $\text{ } y = \frac{13}{4}$