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COMEDK · Maths · 1. Basic of Mathematics

\(\text { If } \dfrac{1}{2}\left(\dfrac{3 x}{5}+4\right) \geq \dfrac{1}{3}(x-6), x \in R \text { then }\)

  1. A \(x \in(120, \infty)\)
  2. B \(x \in(-\infty, 120)\)
  3. C \(x \in(-\infty, 120]\)
  4. D \(x \in[120, \infty)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(x \in(-\infty, 120]\)

Step-by-step Solution

Detailed explanation

Given the inequality \(\dfrac{1}{2}\left(\dfrac{3x}{5} + 4\right) \geq \dfrac{1}{3}(x - 6)\). Multiplying both sides by \(6\) to clear the denominators: \(3\left(\dfrac{3x}{5} + 4\right) \geq 2(x - 6)\) Expanding both sides: \(\dfrac{9x}{5} + 12 \geq 2x - 12\) Rearranging the…