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Mathematics

Solve the following inequation and represent the solution set on the number line:

4x−19<3x5−2≤−25+x,x∈R4x - 19 \lt \dfrac{3x}{5} - 2 \le - \dfrac{2}{5} + x, x ∈ \bold{R}

Linear Inequations

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Answer

Given,

4x−19<3x5−2≤−25+x,x∈R4x−19<3x5−2 and 3x5−2≤−25+x⇒4x−3x5<−2+19 and 3x5−2≤−25+x⇒20x−3x5<17 and −2+25≤x−3x5⇒17x5<17 and −85≤2x5⇒x5<1 and x≥−4⇒x<5 and x≥−4⇒−4≤x<5,x∈R4x-19 \lt \dfrac{3x}{5} - 2 \le - \dfrac{2}{5} + x, x ∈ \bold{R} \\[1em] 4x - 19 \lt \dfrac{3x}{5} -2 \text{ and } \dfrac{3x}{5} - 2 \le - \dfrac{2}{5} + x \\[0.5em] \Rightarrow 4x -\dfrac{3x}{5} \lt -2 + 19 \text{ and } \dfrac{3x}{5} - 2 \le - \dfrac{2}{5} + x \\[0.5em] \Rightarrow \dfrac{20x-3x}{5} \lt 17 \text{ and } -2 + \dfrac{2}{5} \le x - \dfrac{3x}{5} \\[0.5em] \Rightarrow \dfrac{17x}{5} \lt 17 \text{ and } \dfrac{-8}{5} \le \dfrac{2x}{5} \\[0.5em] \Rightarrow \dfrac{x}{5} \lt 1 \text{ and } x \ge -4 \\[0.5em] \Rightarrow x \lt 5 \text{ and } x \ge -4 \\[0.5em] \Rightarrow -4 \le x \lt 5 , x ∈ \bold{R}

Hence, Solution set = {x : x ∈ R, -4 ≤ x < 5}.

The graph of the solution set is represented by thick line starting from -4 (including -4) till 5 (not including 5).

Solve the following inequation and represent the solution set on the number line: 4x - 19 < (3x/5) - 2 ≤ -(2/5) + x, x ∈ R. Linear Inequations, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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