Question

Solve the follow inequality. ∣3x−4∣≥8

Answer 1

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

Answer 2

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-(4)/(3) }`

Therefore, the solutions are

`\mathrm{x\geq 4}\\\mathrm{x\leq \displaystyle-(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}`