Question

The solution set of the inequality |3x| ≥ |6 − 3x| is:

• A. (−∞, 1]
• B. [1, ∞)
• C. (−∞, 1) ∪ (1,∞)
• D. (−∞, −1) ∪ (−1,∞)

Answer 1

The Correct Option is B

The inequality \( |3x| \geq |6 - 3x| \) involves absolute values, so split into cases:

Case 1: \( 3x \geq 6 - 3x \):

\( 3x + 3x \geq 6 \implies 6x \geq 6 \implies x \geq 1 \).

Case 2: \( 3x \leq -(6 - 3x) \):

\( 3x \leq -6 + 3x \implies 0 \leq -6 \),

which is not possible.

Thus, the solution is \( x \geq 1 \), or \([1, \infty)\).