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23-x ≥ x 5+4

Question

$2 (3 - x) \geq \frac{x}{5} + 4$

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Solution

$2 (3 - x) \geq \frac{x}{5} + 4 \Rightarrow 6 - 2 x \geq \frac{x}{5} + 4 \Rightarrow 6 - 4 \geq \frac{x}{5} + 2 x [Transposing - 2 x to the RHS and 4 to the LHS] \Rightarrow 2 \geq \frac{11 x}{5} \Rightarrow \frac{11 x}{5} \leq 2 \Rightarrow x \leq \frac{10}{11} [Mltiplying both the sides by \frac{5}{11}] Thus, the solution set of the given inequation is (- \infty, \frac{10}{11}] .$

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