The values of x which satisfied \(|3x| \ge |6 - 3x|\)
A. \((0, 1]\)
B. \([1, 4]\)
C. \((4, \infty)\)
D. \((-1, 0)\)
E. \((-\infty, 0)\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → B and C only
Both sides are non-negative, so the inequality keeps its direction when both sides are squared:
\(9x^2 \ge (6 - 3x)^2\)
\(9x^2 \ge 36 - 36x + 9x^2\)
\(36x \ge 36\)
\(x \ge 1\)
So the inequality holds exactly for x in \([1, \infty)\); a listed set qualifies only if all its values are at least 1.
Checking the statements
(A) \((0, 1]\) — Incorrect. x = 0.5 is in it, but |1.5| < |4.5|.
(B) \([1, 4]\) — Correct. Every value is at least 1.
(C) \((4, \infty)\) — Correct. Every value is greater than 1.
(D) \((-1, 0)\) — Incorrect. All values are less than 1.
(E) \((-\infty, 0)\) — Incorrect. All values are less than 1.