Hello.
Let's solve the absolute value inequality.
In order to do that, let's imagine that |3x-4| is positive.
Since the absolute value of |3x-4| is 3x-4, we write 3x-4 and solve:
[tex]\mathrm{3x-4\geq 8}[/tex]
Now, move -4 to the right, using the opposite operation:
[tex]\mathrm{3x\geq 8+4}[/tex]
Add:
[tex]\mathrm{3x\geq 12}[/tex]
Divide both sides by 3:
[tex]\mathrm{x\geq 4}[/tex]
However, this is only 1 solution.
Let's imagine that |3x-4| is a negative number.
So, the inequality looks like so:
[tex]\mathrm{-3x+4\geq 8}[/tex]
Move 4 to the right:
[tex]\mathrm{-3x\geq 8-4}[/tex]
[tex]\mathrm{-3x\geq 4}[/tex]
Divide both sides by -3:
[tex]\mathrm{x\leq \displaystyle-\frac{4}{3} }[/tex]
Therefore, the solutions are
[tex]\mathrm{x\geq 4}\\\mathrm{x\leq \displaystyle-\frac{4}{3} }[/tex]
[tex]\bigstar[/tex] Note:
If we divide both sides of an inequality by a negative number, we flip the inequality sign.
I hope this helps you.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
