List the solution set of:
11−2x5≥9−3x8+34,x∈N.\dfrac{11-2x}{5} \ge \dfrac{9-3x}{8} + \dfrac{3}{4}, x ∈ \bold{N}.511−2x≥89−3x+43,x∈N.
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Given,
11−2x5≥9−3x8+34⇒11−2x5≥9−3x+68⇒8(11−2x)≥5(15−3x)⇒88−16x≥75−15x⇒−16x+15x≥75−88⇒−x≥−13⇒x≤13\dfrac{11-2x}{5} \ge \dfrac{9-3x}{8} + \dfrac{3}{4} \\[0.5em] \Rightarrow \dfrac{11-2x}{5} \ge \dfrac{9 - 3x + 6}{8} \\[0.5em] \Rightarrow 8(11 - 2x) \ge 5(15 - 3x) \\[0.5em] \Rightarrow 88 - 16x \ge 75 - 15x \\[0.5em] \Rightarrow - 16x + 15x \ge 75 - 88 \\[0.5em] \Rightarrow - x \ge - 13 \\[0.5em] \Rightarrow x ≤ 13 \\[0.5em]511−2x≥89−3x+43⇒511−2x≥89−3x+6⇒8(11−2x)≥5(15−3x)⇒88−16x≥75−15x⇒−16x+15x≥75−88⇒−x≥−13⇒x≤13
Since, x ∈ NSolution set = {1, 2, 3, 4, 5, ….. , 13}.
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Given x ∈ {1, 2, 3, 4, 5, 6, 7, 9} solve x – 3 < 2x – 1.
List the solution set of the inequation
12+8x>5x−32,x∈Z\dfrac{1}{2} + 8x \gt 5x -\dfrac{3}{2}, x ∈ \bold{Z}21+8x>5x−23,x∈Z
Find the values of x, which satisfy the inequation:
−2≤12−2x3≤156−2 \le \dfrac{1}{2}-\dfrac{2x}{3} \le 1\dfrac{5}{6}−2≤21−32x≤165, x ∈ N.
Graph the solution set on the number line.
If x ∈ W, find the solution set of 35x−2x−13>\dfrac{3}{5} x - \dfrac{2x−1}{3} \gt53x−32x−1> 1. Also graph the solution set on the number line, if possible.
