Step by step
The question
Question: solve 2x + 1 > 9.
This is an inequality.
The sign means greater than.
We want x by itself.
Two things are stuck to x: times 2 and + 1.
The + 1 is on the outside, so it comes off first.
Then the times 2.
1 Remove the + 1
To remove + 1, we take away 1.
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.
+ 1 and − 1 make zero.
Cross them out.
9 − 1 = 8.
Now we have 2x > 8.
2 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, so the sign stays true.
2 divided by 2 is 1.
So just x is left.
8 divided by 2 is 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.
11 is greater than 9.
True!
So the answer works.
Let's look back.
First: remove the + 1.
Then: remove the 2.
Then: show it on a number line.
Last: check.