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Solve : 4x−103≤5x−72,x∈R\dfrac{4x-10}{3} \le \dfrac{5x-7}{2}, x ∈ \bold{R} and represent the solution set on the number line.

Linear Inequations

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Answer

Given,

4x−103≤5x−72⇒4x−103×6≤5x−72×6 ( Multiplying both sides by 6) ⇒8x−20≤15x−21\dfrac{4x−10}{3} \le \dfrac{5x−7}{2}\\[0.5em] \Rightarrow \dfrac{4x-10}{3} \times 6 \le \dfrac{5x-7}{2} \times 6 \text{ ( Multiplying both sides by 6) }\\[0.5em] \Rightarrow 8x - 20 \le 15x - 21

⇒8x−15x≤−21+20⇒−7x≤−1⇒7x≥1⇒x≥17\Rightarrow 8x-15x \le -21 +20\\[0.5em] \Rightarrow -7x \le -1\\[0.5em] \Rightarrow 7x \ge 1\\[0.5em] \Rightarrow x \ge \dfrac{1}{7}

∴ Solution Set = {x : x ∈ R, x ≥ 17\dfrac{1}{7}}

The graph of the solution set is represented by thick black line starting from and including 17\dfrac{1}{7} on the number line.

Solve : (4x - 10) / 3 ≤ (5x - 7) / 2, x ∈ R and represent the solution set on the number line. Linear Inequations, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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