Question

Solve the follow inequality. ∣3x−4∣≥8

Answer 1

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:

$\mathrm{3x-4\geq 8}$

Now, move -4 to the right, using the opposite operation:

$\mathrm{3x\geq 8+4}$

Add:

$\mathrm{3x\geq 12}$

Divide both sides by 3:

$\mathrm{x\geq 4}$

However, this is only 1 solution.

Let's imagine that |3x-4| is a negative number.

So, the inequality looks like so:

$\mathrm{-3x+4\geq 8}$

Move 4 to the right:

$\mathrm{-3x\geq 8-4}$

$\mathrm{-3x\geq 4}$

Divide both sides by -3:

$\mathrm{x\leq \displaystyle-\frac{4}{3} }$

Therefore, the solutions are

$\mathrm{x\geq 4}\\\mathrm{x\leq \displaystyle-\frac{4}{3} }$

$\bigstar$ 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.

$\boxed{imperturbability}$

Answer 2

X>=4
First step- Add 4 to both sides
Simply-3x>=12
Divide both sides by 3- 3x/3 12/3
X>=4 is final answer