Step by step
The question
Question: solve −2 ≤ x − 3 ≤ 1.
x is in the middle, between two numbers.
1 Remove the − 3
We want x by itself.
The − 3 is in the way.
To remove − 3, we add 3.
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.
− 3 and + 3 make zero.
Cross them out.
−2 plus 3 is 1.
1 plus 3 is 4.
Now we have 1 ≤ x ≤ 4.
So x is between 1 and 4: 1 ≤ x ≤ 4.
2 Show it on a number line
Books also write the answer like this.
It is called interval notation.
A square bracket means the end is in, like the filled circle.
3 Check
Let's test one number from the answer: 3.
We put it in place of x in the middle part.
0 is greater than or equal to −2, and less than or equal to 1.
True!
So the answer works.
Let's look back.
First: remove the − 3.
Then: show it on a number line.
Last: check.