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Question

Mathematics Question on Determinants

The solution set of the inequality 37(3x+5)9x8(x3)37 - (3x + 5) \ge 9x - 8 (x - 3) is

A

(,2)(- \infty, 2)

B

(,2)(- \infty, -2)

C

(,2](- \infty, 2]

D

(,2](- \infty, -2]

Answer

(,2](- \infty, 2]

Explanation

Solution

We have, 37(3x+5)9x8(x3)37 - (3x + 5) \ge 9x - 8(x - 3) (373x5)9x8x+24(37 - 3x - 5) \ge 9x - 8x + 24 323xx+24\Rightarrow 32 - 3x \ge x + 24 Transferring the term 2424 to L.H.S.L.H.S. and the term (3x)(-3x) to R.H.S.R.H.S. 3224x+3x84x4x832 - 24 \ge x + 3x \Rightarrow 8 \ge 4x \Rightarrow 4x \le 8 Dividing both sides by 4, 4x484x2\frac{4x}{4} \le\frac{8}{4} \Rightarrow x \le 2 \therefore Solution set is (,2](-\infty, 2].