Step by step
The question
Question: solve 0 ≤ x − 2 < 3.
x is in the middle, between two numbers.
1 Remove the − 2
We want x by itself.
The − 2 is in the way.
To remove − 2, we add 2.
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.
− 2 and + 2 make zero.
Cross them out.
0 plus 2 is 2.
3 plus 2 is 5.
Now we have 2 ≤ x < 5.
So x is between 2 and 5: 2 ≤ x < 5.
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.
A square bracket means the end is in, like the filled circle.
3 Check
Let's test one number from the answer: 4.
We put it in place of x in the middle part.
2 is greater than or equal to 0, and less than 3.
True!
So the answer works.
Let's look back.
First: remove the − 2.
Then: show it on a number line.
Last: check.