# How do you solve -5abs(4y-11)-3=12?

Sep 1, 2016

No solution.

#### Explanation:

$- 5 | 4 y - 11 | - 3 = 12$ can be written as

$- 5 | 4 y - 11 | = 12 + 3 = 15$

or $| 4 y - 11 | = \frac{15}{-} 5 = - 3$

As absolute value of a number cannot be negative there is no solution.

Sep 1, 2016

The solution of $x$ is $\left[\frac{7}{4} , 2\right]$

#### Explanation:

This is an Inequatlity problem. The general forms is:
$\left\mid x - a \right\mid = b$
$- b \le \left(x - a\right) \le b$
$\left(a - b\right) \le x \le \left(a + b\right)$
Thus, $x$ has a solution range [(a-b)$,$(a+b)]

The solution to this problem goes like:

$- 5 \left\mid 4 y - 11 \right\mid - 3 = 12$ ;or
$- 5 \left\mid 4 y - 11 \right\mid = 15$ ;or
$\left\mid 4 y - 11 \right\mid = - 3$ ;or
$- \left(- 3\right) \le 4 y - 11 \le - 3$ ;or
$\left(11 + 3\right) \le 4 y \le \left(11 - 3\right)$ ;or
$14 \le 4 y \le 8$ ;or
$\frac{7}{4} \le y \le 2$
Thus, the solution range of $x$ is $\left[\frac{7}{4} , 2\right]$