melandnick2001
Answered

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Solve the follow inequality. ∣3x−4∣≥8

Sagot :

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]

ariannasmith006
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
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