Step by step
The question
Question: solve 2x − 1 > 3 or x + 2 > 0.
"Or" means one of the parts is enough.
1 Solve the first part
First part: 2x − 1 > 3.
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.
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.
Now we have 2x > 4.
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.
4 divided by 2 is 2.
So x is greater than 2.
2 Solve the second part
Second part: x + 2 > 0.
We want x by itself.
The + 2 is in the way.
To remove + 2, we take away 2.
We do it on both sides, so the sign stays true.
+ 2 and − 2 make zero.
Cross them out.
0 − 2 = −2.
So x is greater than −2.
3 Show each part on a number line
4 Put the parts together
"Or": we keep every number that is shaded on either line.
So x > −2.
Careful!
"Or" means one part is enough.
A number that is shaded on one line works.
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.
5 Check
Let's test one number from the answer: −1.
1 is greater than 0.
True!
So the answer works.
Let's look back.
First: solve the first part.
Then: solve the second part.
Then: show each part on a number line.
Then: put the parts together.
Last: check.