Two Conditions at Once

"$x$ is greater than 1 and $x$ is less than 5" is two conditions on one number, and both must be true. You can write the two conditions as one line, with $x$ in the middle. This form is called a chain:

$$1 < x < 5$$

Read it from the middle. $x$ is greater than 1 and less than 5. The solutions are all the numbers between 1 and 5, not including 1 or 5. On the number line, this is a segment with an open dot at each end.

1 < x < 5: between 1 and 5, both ends open

An end of a chain can be included too. $-2 \le x < 3$ includes -2, so the dot at -2 is filled. It does not include 3, so the dot at 3 is open. Both signs in a chain must point the same way. $1 < x < 5$ and $5 > x > 1$ are both correct, and they mean the same thing. Never mix a < and a > in one chain.