Solve |3x| <= 12 Step by Step | Absolute value inequalities

Step by step

The question

Question: solve |3x| ≤ 12.

|3x| ≤ 12

1 Draw the distance

2 Write it without bars

So 3x is between −12 and 12: −12 ≤ 3x ≤ 12.

Now x is in the middle.

−12 ≤ 3x ≤ 12

3 Remove the 3

3x means 3 times x.

We want just x.

To remove times 3, we divide by 3.

We do it to all three parts.

3 is a positive number, so the signs stay the same.

−123 ≤ 3x3 ≤ 123

3 divided by 3 is 1.

So just x is left.

−12 divided by 3 is −4.

12 divided by 3 is 4.

−123 = −4, 123 = 4

Now we have −4 ≤ x ≤ 4.

So x is between −4 and 4: −4 ≤ x ≤ 4.

−4 ≤ x ≤ 4

4 Show it on a number line

Books also write the answer like this.

It is called interval notation.

A square bracket means the end is in, like the filled circle.

interval: [−4, 4]

5 Check

Let's test one number from the answer: 1.

We put it in the question.

The inside is 3, and the bars make it 3.

x = 1: |3(1)| = |3| = 3

3 is less than or equal to 12.

True!

So the answer works.

3 ≤ 12

Let's look back.

First: draw the distance.

Then: write it without bars.

Then: remove the 3.

Then: show it on a number line.

Last: check.

Answer