Step by step
The question
Question: solve x + 2 > 1 and x − 3 < 4.
"And" means both parts must be true.
1 Solve the first part
First part: x + 2 > 1.
We want x by itself.
The + 2 is in the way.
To remove + 2, we take away 2.
We do it on both sides, so the sign stays true.
+ 2 and − 2 make zero.
Cross them out.
1 − 2 = −1.
So x is greater than −1.
2 Solve the second part
Second part: x − 3 < 4.
We want x by itself.
The − 3 is in the way.
To remove − 3, we add 3.
We do it on both sides, so the sign stays true.
− 3 and + 3 make zero.
Cross them out.
4 + 3 = 7.
So x is less than 7.
3 Show each part on a number line
4 Find the numbers in both
"And": we keep only the numbers that are shaded on both lines.
So −1 < x < 7.
x is between −1 and 7.
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.
5 Check
Let's test one number from the answer: 3.
"And": it must work in both parts.
First part.
5 is greater than 1.
True!
Now the second part.
0 is less than 4.
True!
So the answer works.
Let's look back.
First: solve the first part.
Then: solve the second part.
Then: show each part on a number line.
Then: find the numbers in both.
Last: check.