Step by step
The question
Question: solve 2 ≤ 3x − 4 ≤ 11.
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 add 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.
2 plus 4 is 6.
11 plus 4 is 15.
Now we have 6 ≤ 3x ≤ 15.
2 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it to all three parts.
3 is a positive number, so the signs stay the same.
3 divided by 3 is 1.
So just x is left.
6 divided by 3 is 2.
15 divided by 3 is 5.
Now we have 2 ≤ x ≤ 5.
So x is between 2 and 5: 2 ≤ x ≤ 5.
3 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.
4 Check
Let's test one number from the answer: 4.
We put it in place of x in the middle part.
8 is greater than or equal to 2, and less than or equal to 11.
True!
So the answer works.
Let's look back.
First: remove the − 4.
Then: remove the 3.
Then: show it on a number line.
Last: check.