Question

The set of all real \( x \) satisfying the inequality \[ \frac{3 - |x|}{4 - |x|} \geq 0 \] is

• A. \( [-3, 3] \cup (-4, 4) \)
• B. \( (-4, 4) \)
• C. \( [-3, 3] \cup (4, \infty) \)
• D. \( (-3, 3] \cup (-4, \infty) \)

Hint:

For inequalities involving absolute values, break the expression into intervals based on the behavior of the absolute value function.

Answer 1

The Correct Option is A

Step 1: Analyze the inequality.
The inequality involves absolute values, so we need to break it into different intervals based on \( |x| \).
Step 2: Conclusion.
The solution set is \( [-3, 3] \cup (-4, 4) \). Final Answer: \[ \boxed{[-3, 3] \cup (-4, 4)} \]