Solve x > -2 and x < 3

Step by step

The question

Question: solve x > −2 and x < 3.

"And" means both parts must be true.

Both parts are solved already: x is by itself in each one.

1 Show each part on a number line

2 Find the numbers in both

"And": we keep only the numbers that are shaded on both lines.

So −2 < x < 3.

x is between −2 and 3.

Careful!

A number that is shaded on only one line is not an answer.

It must be on both.

Books also write the answer like this.

It is called interval notation.

A round bracket means the end is not in, like the open circle.

3 Check

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

"And": it must work in both parts.

First part.

1 is greater than −2.

True!

Now the second part.

1 is less than 3.

True!

So the answer works.

Let's look back.

First: show each part on a number line.

Then: find the numbers in both.

Last: check.