Answer
$[-2,-\displaystyle \frac{2}{9}]$
Work Step by Step
4 times a number is subtracted from 5 can be written as: $5-4x $
The absolute value of the difference $|5-4x|$ is at most 13:
$|5-4x|\leq 13$
$|5-4x|=|4x-5| \qquad $, because $|a-b|=|b-a|$
So, we solve
$|4x-5|\leq 13$
$|u| \leq c $ is equivalent to $-c \leq u \leq c.$
$-13\leq 4x-5\leq 13\qquad.../+5$
$-8\leq 4x\leq 18 \qquad.../\div 4$
$-2\displaystyle \leq x\leq\frac{9}{2}$
Borders are included:
Solution set: $[-2,-\displaystyle \frac{2}{9}]$
