Step by step
The question
Question: solve −x > 4.
This is an inequality.
The sign means greater than.
1 Remove the −1
−x means −1 times x.
We want just x.
To remove times −1, we divide by −1.
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.
Greater than becomes less than.
−1 divided by −1 is 1.
So just x is left.
4 divided by −1 is −4.
So x is less than −4.
Careful!
Many people forget to turn the sign.
They get x > −4.
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: −5.
We put it in place of x.
First the left side.
Now the right side.
5 is greater than 4.
True!
So the answer works.
Let's look back.
First: remove the −1.
Then: show it on a number line.
Last: check.