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