Step by step
The question
Question: solve 3 < 2x + 1 < 9.
x is in the middle, between two numbers.
1 Remove the + 1
We want x by itself.
The + 1 is in the way.
To remove + 1, we take away 1.
We do it to all three parts.
Why all three?
The signs compare the three parts.
If we change only one part, the answer can change.
+ 1 and − 1 make zero.
Cross them out.
3 minus 1 is 2.
9 minus 1 is 8.
Now we have 2 < 2x < 8.
2 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it to all three parts.
2 is a positive number, so the signs stay the same.
2 divided by 2 is 1.
So just x is left.
2 divided by 2 is 1.
8 divided by 2 is 4.
Now we have 1 < x < 4.
So x is between 1 and 4: 1 < x < 4.
3 Show it on a number line
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.
We put it in place of x in the middle part.
7 is greater than 3, and less than 9.
True!
So the answer works.
Let's look back.
First: remove the + 1.
Then: remove the 2.
Then: show it on a number line.
Last: check.