Answer:
We conclude that
[tex]3x-11>7x+9\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-5\right)\end{bmatrix}[/tex]
Please check the attached diagram which shows the solution on the number line.
Step-by-step explanation:
Given the inequality
[tex]3x-11>7x+9[/tex]
Add 11 to both sides
[tex]3x-11+11>7x+9+11[/tex]
Simplify
[tex]3x>7x+20[/tex]
Subtract 7 from both sides
[tex]3x-7x>7x+20-7x[/tex]
Simplify
[tex]-4x>20[/tex]
Multiply both sides by -1 (reverses the inequality)
[tex]\left(-4x\right)\left(-1\right)<20\left(-1\right)[/tex]
Simplify
[tex]4x<-20[/tex]
Divide both sides by 4
[tex]\frac{4x}{4}<\frac{-20}{4}[/tex]
Simplify
[tex]x<-5[/tex]
Therefore, we conclude that
[tex]3x-11>7x+9\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-5\right)\end{bmatrix}[/tex]
Please check the attached diagram which shows the solution on the number line.
