Step by step
The question
Question: solve 2x + 1 > 5 and 2x + 1 < 3.
"And" means both parts must be true.
1 Solve the first part
First part: 2x + 1 > 5.
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 take away 1.
We do it on both sides, so the sign stays true.
+ 1 and − 1 make zero.
Cross them out.
5 − 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: 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 take away 1.
We do it on both sides, so the sign stays true.
+ 1 and − 1 make zero.
Cross them out.
3 − 1 = 2.
Now we have 2x < 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.
2 divided by 2 is 1.
So x is less than 1.
3 Show each part on a number line
4 Find the numbers in both
No number is shaded on both lines.
No number is in both parts.
So there is no solution.
Let's look back.
First: solve the first part.
Then: solve the second part.
Then: show each part on a number line.
Last: find the numbers in both.