Question

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

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

Answer 1

Answer: (B)

[1, ∞)

Answer 2

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 $[1, \infty)$.