The inequality provided in the image is a compound inequality:

$x > 79 \text{ and } x < 82$

This means that $x$ lies between 79 and 82, but does not include either endpoint.

To represent this on a number line:

• You would place open circles (since the inequality is strict, using $>$ and $<$ rather than $\geq$ or $\leq$) at both 79 and 82.
• Then, shade the region between 79 and 82, indicating that $x$ can take any value between them but not equal to 79 or 82.

To graph it on the number line:

• Place an open circle at 79.
• Place another open circle at 82.
• Draw a line segment between 79 and 82.

This visually represents the solution set: all numbers between 79 and 82 but excluding 79 and 82 themselves.

Would you like more details on inequalities or any other related topic? Here are 5 related questions for further exploration:

1. What is the difference between strict and non-strict inequalities?
2. How would the graph change if the inequality were (x \geq 79 \text{ and } x \leq