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Mathematics

Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line.

Linear Inequations

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Answer

Given,

2x−5≤5x+4<11⇒2x−5≤5x+4 and 5x+4<11⇒2x−5−4≤5x and 5x+4<11⇒2x−9≤5x and 5x<11−4⇒2x−5x≤9 and 5x<7⇒−3x≤9 and x<75⇒3x≥−9 and x<75⇒x≥−3 and x<1.4∴−3≤x<1.42x - 5 \le 5x + 4 \lt 11 \\[0.5em] \Rightarrow 2x - 5 \le 5x + 4 \text { and } 5x + 4 \lt 11 \\[0.5em] \Rightarrow 2x - 5 - 4 \le 5x \text { and } 5x + 4 \lt 11 \\[0.5em] \Rightarrow 2x - 9 \le 5x \text{ and } 5x \lt 11 - 4 \\[0.5em] \Rightarrow 2x - 5x \le 9 \text{ and } 5x \lt 7 \\[0.5em] \Rightarrow -3x \le 9 \text{ and } x \lt \dfrac{7}{5} \\[0.5em] \Rightarrow 3x \ge - 9 \text{ and } x \lt \dfrac{7}{5} \\[0.5em] \Rightarrow x \ge - 3 \text{ and } x \lt 1.4 \\[0.5em] \therefore -3 \le x \lt 1.4

∴ Solution set = {-3, -2, -1, 0, 1}

The graph of the solution set is represented by thick black dots on the number line.

Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line. Linear Inequations, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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