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Mathematics

Solve the inequation :

12+156x≤5+3x12 + 1\dfrac{5}{6}x \le 5 + 3x and x ∈ R.

Linear Inequations

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Answer

Given,

⇒12+156x≤5+3x⇒12+116x≤5+3x⇒3x−116x≥12−5⇒18x−11x6≥7⇒7x6≥7⇒x≥7×67⇒x≥6.\Rightarrow 12 + 1\dfrac{5}{6}x \le 5 + 3x \\[1em] \Rightarrow 12 + \dfrac{11}{6}x \le 5 + 3x \\[1em] \Rightarrow 3x - \dfrac{11}{6}x \ge 12 - 5 \\[1em] \Rightarrow \dfrac{18x - 11x}{6} \ge 7 \\[1em] \Rightarrow \dfrac{7x}{6} \ge 7 \\[1em] \Rightarrow x \ge \dfrac{7 \times 6}{7} \\[1em] \Rightarrow x \ge 6.

∴ Solution set = {x : x ∈ R and x ≥ 6}.

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