COMEDK · Maths · 1. Basic of Mathematics
\(\text { If } \dfrac{1}{2}\left(\dfrac{3 x}{5}+4\right) \geq \dfrac{1}{3}(x-6), x \in R \text { then }\)
- A \(x \in(120, \infty)\)
- B \(x \in(-\infty, 120)\)
- C \(x \in(-\infty, 120]\)
- D \(x \in[120, \infty)\)
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…
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