Step by step
The question
Question: solve 6 < 2x.
This is an inequality.
The sign means less than.
Let's swap the two sides, so x is on the left.
When we swap, the sign turns around too.
Less than becomes greater than.
1 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
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.
2 divided by 2 is 1.
So just x is left.
6 divided by 2 is 3.
So x is greater than 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.
3 Check
Let's test one number from the answer: 4.
We put it in place of x.
First the left side.
Now the right side.
6 is less than 8.
True!
So the answer works.
Let's look back.
First: remove the 2.
Then: show it on a number line.
Last: check.