Step by step
The question
Question: solve x + 3 > 7.
This is an inequality.
The sign means greater than.
x + 3 > 7
1 Remove the + 3
We want x by itself.
The + 3 is in the way.
To remove + 3, we take away 3.
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.
x + 3 − 3 > 7 − 3
+ 3 and − 3 make zero.
Cross them out.
7 − 3 = 4.
7 − 3 = 4
So x is greater than 4.
x > 4
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.
interval: (4, ∞)
3 Check
Let's test one number from the answer: 5.
We put it in place of x.
First the left side.
Left: 5 + 3 = 8
Now the right side.
Right: 7
8 is greater than 7.
True!
So the answer works.
8 > 7
Let's look back.
First: remove the + 3.
Then: show it on a number line.
Last: check.
Answer
x > 4