Answer:
we conclude that:
[tex]8\le \:-4x<20\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-5<x\le \:-2\:\\ \:\mathrm{Interval\:Notation:}&\:(-5,\:-2]\end{bmatrix}[/tex]
The graph is also attached below.
Step-by-step explanation:
Given the inequality expression
[tex]9\le 1-4x<21[/tex]
simplify
[tex]9\le -4x+1<\:21[/tex]
Add -1 to all parts
[tex]9+(-1)\le -4x+1+(-1)<\:21+(-1)[/tex]
simplify
[tex]8\le -4x<\:20[/tex]
Divide all parts by -4
[tex]\frac{8}{-4}\le -\frac{4x}{-4}<\:\frac{20}{-4}[/tex]
[tex]-2\ge \:x>-5[/tex]
Thus, we conclude that:
[tex]8\le \:-4x<20\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-5<x\le \:-2\:\\ \:\mathrm{Interval\:Notation:}&\:(-5,\:-2]\end{bmatrix}[/tex]
The graph is also attached below.
