Solve x - 2 <= 5

Step by step

The question

Question: solve x − 2 ≤ 5.

This is an inequality.

The sign means less than or equal to.

1 Remove the − 2

We want x by itself.

The − 2 is in the way.

To remove − 2, we add 2.

We do it on both sides.

Why both sides?

The sign compares the two sides.

If we change only one side, the answer can change.

− 2 and + 2 make zero.

Cross them out.

5 + 2 = 7.

So x is less than or equal to 7.

2 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.

∞ means it goes on for ever.

3 Check

Let's test one number from the answer: 6.

We put it in place of x.

First the left side.

Now the right side.

4 is less than or equal to 5.

True!

So the answer works.

Let's look back.

First: remove the − 2.

Then: show it on a number line.

Last: check.