Step by step
The question
Question: solve x > 1 and x > 4.
"And" means both parts must be true.
Both parts are solved already: x is by itself in each one.
1 Show each part on a number line
2 Find the numbers in both
"And": we keep only the numbers that are shaded on both lines.
So x > 4.
Careful!
The answer is not between the two numbers.
Both parts must be true, so only the numbers shaded on both lines count.
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: 5.
"And": it must work in both parts.
First part.
5 is greater than 1.
True!
Now the second part.
5 is greater than 4.
True!
So the answer works.
Let's look back.
First: show each part on a number line.
Then: find the numbers in both.
Last: check.