Step by step
The question
Question: solve 2x < 6 and x + 1 > 0.
"And" means both parts must be true.
1 Solve the first part
First part: 2x < 6.
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so the sign stays true.
2 divided by 2 is 1.
So just x is left.
6 divided by 2 is 3.
So x is less than 3.
2 Solve the second part
Second part: x + 1 > 0.
We want x by itself.
The + 1 is in the way.
To remove + 1, we take away 1.
We do it on both sides, so the sign stays true.
+ 1 and − 1 make zero.
Cross them out.
0 − 1 = −1.
So x is greater than −1.
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 < 3.
x is between −1 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.
5 Check
Let's test one number from the answer: 1.
"And": it must work in both parts.
First part.
2 is less than 6.
True!
Now the second part.
2 is greater than 0.
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.