The solution set is not the empty set for which one of the following inequalities?

Question

Quizplus · Accepted Answer

For an inequality to have a solution set, it means that there exists at least one value of the variable that satisfies the inequality. We can see that options A, B, and D have variables raised to even powers, which means that the expressions inside the absolute value function will always be non-negative. Therefore, the absolute value function will always return non-negative values, which means that the inequality cannot be satisfied and the solution set is empty. However, option C has a variable raised to an odd power, which means that the expression inside the absolute value function can be negative for certain values of the variable. Therefore, there exists at least one value of the variable that satisfies the inequality, and the solution set is not empty.

The Solution Set Is Not the Empty Set for Which