Step by step
The question
Question: solve 2x < −4 or 2x > 6.
Two inequalities, joined by "or".
"Or" means: x can make one of them true, or the other.
We solve both, side by side.
1 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
In each one, on both sides.
2 is a positive number, so the sign stays the same.
2 divided by 2 is 1.
So just x is left.
−4 divided by 2 is −2.
6 divided by 2 is 3.
So x < −2 or x > 3.
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.
∪ means or.
3 Check
Let's test one number from each part.
First −3, from the left part.
−6 is less than −4.
True!
Now 4, from the right part.
8 is greater than 6.
True!
Both parts work!
Let's look back.
First: remove the 2.
Then: show it on a number line.
Last: check.