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Mathematics

Find the smallest value of x for which 5 - 2x < 512−53x5\dfrac{1}{2} - \dfrac{5}{3}x, where x is an integer.

Linear Inequations

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Answer

Given,

⇒5−2x<512−53x⇒5−2x<112−53x⇒5−112<−53x+2x⇒10−112<−5x+6x3⇒−12<x3⇒x3×3>−12×3⇒x>−32⇒x>−1.5\Rightarrow 5 - 2x \lt 5\dfrac{1}{2} - \dfrac{5}{3}x \\[1em] \Rightarrow 5 - 2x \lt \dfrac{11}{2} - \dfrac{5}{3}x \\[1em] \Rightarrow 5 - \dfrac{11}{2} \lt -\dfrac{5}{3}x + 2x \\[1em] \Rightarrow \dfrac{10 - 11}{2} \lt \dfrac{-5x + 6x}{3} \\[1em] \Rightarrow -\dfrac{1}{2} \lt \dfrac{x}{3} \\[1em] \Rightarrow \dfrac{x}{3} \times 3 \gt -\dfrac{1}{2} \times 3 \\[1em] \Rightarrow x \gt -\dfrac{3}{2} \\[1em] \Rightarrow x \gt -1.5

Since, x is an integer.

Hence, smallest value of x = -1.

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