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Mathematics

Solve the inequation :

5x+17−4(x7+25)≤135+3x−17,x∈R.\dfrac{5x+1}{7} - 4\Big(\dfrac{x}{7}+ \dfrac{2}{5}\Big) \le 1\dfrac{3}{5}+\dfrac{3x-1}{7}, x ∈ \bold{R}.

Linear Inequations

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Answer

Given,

5x+17−4(x7+25)≤135+3x−17,x∈R.\dfrac{5x+1}{7} - 4\Big(\dfrac{x}{7}+ \dfrac{2}{5}\Big) \le 1\dfrac{3}{5}+\dfrac{3x-1}{7}, x ∈ \bold{R}.

Multiplying both sides by 35

⇒25x+5−4(5x+14)≤56+15x−5⇒25x+5−20x−56≤56+15x−5⇒5x−51≤51+15x⇒5x−15x≤51+51⇒−10x≤102⇒x≥−10210⇒x≥−515\Rightarrow 25x + 5-4(5x + 14) \le 56 + 15x -5 \\[0.5em] \Rightarrow 25x + 5 - 20x - 56 \le 56 + 15x -5 \\[0.5em] \Rightarrow 5x - 51 \le 51 + 15x \\[0.5em] \Rightarrow 5x - 15x \le 51 + 51 \\[0.5em] \Rightarrow -10x \le 102 \\[0.5em] \Rightarrow x \ge -\dfrac{102}{10} \\[0.5em] \Rightarrow x \ge -\dfrac{51}{5}

∴ Solution set = {x : x ∈ R, x ≥−515\ge -\dfrac{51}{5} }.

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