Step by step
The question
Question: solve |3x + 3| > 6.
1 Draw the distance
2 Write it without bars
So 3x + 3 < −6 or 3x + 3 > 6.
"Or" means: x can make one of them true, or the other.
We solve both, side by side.
3 Remove the + 3
We want x by itself.
The + 3 is in the way.
In each one, we take away 3 on both sides.
+ 3 and − 3 make zero, in both.
−6 minus 3 is −9.
6 minus 3 is 3.
Now we have 3x < −9 or 3x > 3.
4 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
In each one, on both sides.
3 is a positive number, so the sign stays the same.
3 divided by 3 is 1.
So just x is left.
−9 divided by 3 is −3.
3 divided by 3 is 1.
So x < −3 or x > 1.
5 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.
6 Check
Let's test one number from each part, in the question.
First −4.
9 is greater than 6.
True!
Now 2, from the right part.
9 is greater than 6.
True!
Both parts work!
Let's look back.
First: draw the distance.
Then: write it without bars.
Then: remove the + 3.
Then: remove the 3.
Then: show it on a number line.
Last: check.