Step by step
The question
Question: solve |5x| > 10.
1 Draw the distance
2 Write it without bars
So 5x < −10 or 5x > 10.
"Or" means: x can make one of them true, or the other.
We solve both, side by side.
3 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
In each one, on both sides.
5 is a positive number, so the sign stays the same.
5 divided by 5 is 1.
So just x is left.
−10 divided by 5 is −2.
10 divided by 5 is 2.
So x < −2 or x > 2.
4 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.
∪ means or.
5 Check
Let's test one number from each part, in the question.
First −3.
15 is greater than 10.
True!
Now 3, from the right part.
15 is greater than 10.
True!
Both parts work!
Let's look back.
First: draw the distance.
Then: write it without bars.
Then: remove the 5.
Then: show it on a number line.
Last: check.