Step by step
The question
Question: solve −3x < 9.
This is an inequality.
The sign means less than.
1 Remove the −3
−3x means −3 times x.
We want just x.
To remove times −3, we divide by −3.
We do it on both sides.
Why both sides?
The sign compares the two sides.
If we change only one side, the answer can change.
We divide by a negative number.
That turns the sign around.
Less than becomes greater than.
−3 divided by −3 is 1.
So just x is left.
9 divided by −3 is −3.
So x is greater than −3.
Careful!
Many people forget to turn the sign.
They get x < −3.
But we divided by a negative number.
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.
∞ means it goes on for ever.
3 Check
Let's test one number from the answer: −2.
We put it in place of x.
First the left side.
Now the right side.
6 is less than 9.
True!
So the answer works.
Let's look back.
First: remove the −3.
Then: show it on a number line.
Last: check.