Step by step
The question
Question: solve 2(x − 1) > 6.
This is an inequality.
The sign means greater than.
1 Remove the 2
The 2 multiplies the whole bracket.
Easy way: remove the 2 first.
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 is a positive number, so the sign stays the same.
2 divided by 2 is 1.
So just the bracket is left.
6 divided by 2 is 3.
Now we have x − 1 > 3.
We don't need the bracket any more.
2 Remove the − 1
We want x by itself.
The − 1 is in the way.
To remove − 1, we add 1.
We do it on both sides, so the sign stays true.
− 1 and + 1 make zero.
Cross them out.
3 + 1 = 4.
So x is greater than 4.
3 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.
4 Check
Let's test one number from the answer: 5.
We put it in place of x.
First the left side.
Now the right side.
8 is greater than 6.
True!
So the answer works.
Let's look back.
First: remove the 2.
Then: remove the − 1.
Then: show it on a number line.
Last: check.