Step by step
The question
Question: solve −6 < 3x < 12.
x is in the middle, between two numbers.
−6 < 3x < 12
1 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.
−63 < 3x3 < 123
3 divided by 3 is 1.
So just x is left.
−6 divided by 3 is −2.
12 divided by 3 is 4.
−63 = −2, 123 = 4
Now we have −2 < x < 4.
So x is between −2 and 4: −2 < x < 4.
−2 < x < 4
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.
interval: (−2, 4)
3 Check
Let's test one number from the answer: 1.
We put it in place of x in the middle part.
Middle: 3(1) = 3
3 is greater than −6, and less than 12.
True!
So the answer works.
−6 < 3 < 12
Let's look back.
First: remove the 3.
Then: show it on a number line.
Last: check.
Answer
−2 < x < 4