Question

solve the following inequality, and graph the solution set.$|x| < 3$$\bigcirc$ b. the solution set is $emptyset$.choose the correct graph.$\bigcirc$ a.$\bigcirc$ b.$\bigcirc$ c.$\bigcirc$ d.$\bigcirc$ e.$\bigcirc$ f.

Explanation:

Step1: Rewrite absolute value inequality

For $|x| < a$ where $a>0$, this is equivalent to $-a < x < a$.
So $|x| < 3$ becomes $-3 < x < 3$.

Step2: Match to correct graph

The solution is all real numbers between -3 and 3, which corresponds to an open interval (open circles at -3 and 3, shaded between them).

Answer:

D. <The graph with an open interval shaded between -3 and 3 on the number line>