At the base of a mountain, a rock climber begins at ground level and descends 23 feet to explore an underground cave. After returning to ground level from the cave, the climber ascends 45 feet up the mountain. Which inequality correctly compares the elevations of the climber down in the cave and up on the mountain?

These are expressions where one or more variables are related through signs different than the equal sign. Unlike equations, inequalities often result in ranges of solutions or intervals. Some special rules also don't apply to equations and not on inequalities and vice-versa.

The conditions stated in the problem tell us that the rock climber begins at ground level, which we'll assume as y=0. Then he descends to y = -23 ft, goes up to ground level and finally ascends to y = 45 ft. We can see there are two limits through which the climber moved all the time.

The elevation never was less than -23 and never was greater than 45. It can be written as

[tex]y\geq -23\ and\ y\leq 45[/tex]

Those expressions can be joined in a single relation:

[tex]\boxed{-23\leq y\leq 45}[/tex]