Answer:
The solution is:
[tex]-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}[/tex]
Please check the attached line graph below.
Step-by-step explanation:
Given the expression
[tex]-7r-4\ge \:4r+2[/tex]
Add 4 to both sides
[tex]-7r-4+4\ge \:4r+2+4[/tex]
Simplify
[tex]-7r\ge \:4r+6[/tex]
Subtract 4r from both sides
[tex]-7r-4r\ge \:4r+6-4r[/tex]
Simplify
[tex]-11r\ge \:6[/tex]
Multiply both sides by -1 (reverses the inequality)
[tex]\left(-11r\right)\left(-1\right)\le \:6\left(-1\right)[/tex]
Simplify
[tex]11r\le \:-6[/tex]
Divide both sides by 11
[tex]\frac{11r}{11}\le \frac{-6}{11}[/tex]
Simplify
[tex]r\le \:-\frac{6}{11}[/tex]
Therefore, the solution is:
[tex]-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}[/tex]
Please check the attached line graph below.
