Question

1. provide an example of a compound inequality that, when solved and graphed, has no solution. hint: you saw a couple of examples where the solution was all numbers—think of those cases and try to come up with the opposite.

Explanation:

Step1: Choose conflicting inequalities

Pick two inequalities that cannot both be true for any real number. For example, a number cannot be greater than 5 AND less than 2 at the same time.

Step2: Form compound inequality

Combine the two inequalities with the "and" connector, since "and" requires both conditions to be satisfied simultaneously.
$x > 5 \text{ and } x < 2$

Step3: Verify no solution

There is no real number that is both greater than 5 and less than 2, so this compound inequality has no solution.

Answer:

An example is $\boldsymbol{x > 5 \text{ and } x < 2}$ (or equivalent forms like $2 > x > 5$)