Question

Which of the following is the solution?

A. 2
B. 5≤x<−2

C. 2≤x≤5

D. −5

Answer 1

we conclude that:

`8\le \:-4x<20\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-5<x\le \:-2\:\\ \:\mathrm{Interval\:Notation:}&\:(-5,\:-2]\end{bmatrix}`

The graph is also attached below.

Explanation:

Given the inequality expression

`9\le 1-4x<21`

simplify

`9\le -4x+1<\:21`

Add -1 to all parts

`9+(-1)\le -4x+1+(-1)<\:21+(-1)`

simplify

`8\le -4x<\:20`

Divide all parts by -4

`(8)/(-4)\le -(4x)/(-4)<\:(20)/(-4)`

`-2\ge \:x>-5`

Thus, we conclude that:

`8\le \:-4x<20\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-5<x\le \:-2\:\\ \:\mathrm{Interval\:Notation:}&\:(-5,\:-2]\end{bmatrix}`

The graph is also attached below.