Solve |x/2| <= 4

Step by step

The question

Question: solve |x/2| ≤ 4.

1 Draw the distance

2 Write it without bars

So x/2 is between −4 and 4: −4 ≤ x/2 ≤ 4.

Now x is in the middle.

3 Remove the fraction

The bottom number is 2.

Times 2 will remove it.

We multiply all three parts by 2.

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

2/2 is 1.

The fraction is gone.

2 times −4 is −8.

2 times 4 is 8.

Now we have −8 ≤ x ≤ 8.

So x is between −8 and 8: −8 ≤ x ≤ 8.

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.

5 Check

Let's test one number from the answer: 2.

We put it in the question.

The inside is 1, and the bars make it 1.

1 is less than or equal to 4.

True!

So the answer works.

Let's look back.

First: draw the distance.

Then: write it without bars.

Then: remove the fraction.

Then: show it on a number line.

Last: check.