Step by step
The question
Question: solve 4|x| − 3 > 9.
1 Get the bars alone
We want the bars by themselves.
The − 3 is in the way, so we add 3 on both sides.
− 3 and + 3 make zero.
Cross them out.
9 plus 3 is 12.
To remove times 4, we divide both sides by 4.
4 is a positive number, so the sign stays the same.
4 divided by 4 is 1.
So just the bars is left.
12 divided by 4 is 3.
2 Draw the distance
3 Write it without bars
So x < −3 or x > 3.
"Or" means: x can make one of them true, or the other.
We solve both, side by side.
So x < −3 or x > 3.
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 −4.
13 is greater than 9.
True!
Now 4, from the right part.
13 is greater than 9.
True!
Both parts work!
Let's look back.
First: get the bars alone.
Then: draw the distance.
Then: write it without bars.
Then: show it on a number line.
Last: check.