Step by step
The question
Question: solve 1 < x + 4 < 6.
x is in the middle, between two numbers.
1 Remove the + 4
We want x by itself.
The + 4 is in the way.
To remove + 4, we take away 4.
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.
+ 4 and − 4 make zero.
Cross them out.
1 minus 4 is −3.
6 minus 4 is 2.
Now we have −3 < x < 2.
So x is between −3 and 2: −3 < x < 2.
2 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.
3 Check
Let's test one number from the answer: 1.
We put it in place of x in the middle part.
5 is greater than 1, and less than 6.
True!
So the answer works.
Let's look back.
First: remove the + 4.
Then: show it on a number line.
Last: check.