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A = {x : 11x - 5 > 7x + 3, x ∈ R } and
B = {x : 18x - 9 ≥ 15 + 12x, x ∈ R }.
Find set A ∩ B and represent it on a number line.

Linear Inequations

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Answer

A=x:11x−5>7x+3,x∈RB=x:18x−9≥15+12x,x∈RNow, A=11x−5>7x+3⇒11x−7x>3+5⇒4x>8⇒x>2,x∈RB=18x−9≥15+12x⇒18x−12x≥15+9⇒6x≥24⇒x≥4∴A∩B={x:x∈R,x≥4}\text{A} = {x : 11x - 5 \gt 7x + 3, x ∈ \bold{R}} \\[0.5em] \text{B} = {x : 18x - 9 \ge 15 + 12x, x ∈ \bold{R}} \\[1em] \text{Now, A} = 11x - 5 \gt 7x + 3 \\[0.5em] \Rightarrow 11x - 7x \gt 3 + 5 \\[0.5em] \Rightarrow 4x \gt 8 \\[0.5em] \Rightarrow x \gt 2, x ∈ \bold{R} \\[1em] B= 18x - 9 \ge 15 + 12x \\[0.5em] \Rightarrow 18x -12x \ge 15 + 9 \\[0.5em] \Rightarrow 6x \ge 24 \\[0.5em] \Rightarrow x \ge 4 \\[0.5em] \therefore \text{A} ∩ \text{B} = {x : x ∈ \bold{R}, x \ge 4}

The graph is represented by a thick back line starting from 4 (including 4)

A = {x : 11x - 5 > 7x + 3, x ∈ R } and B = {x : 18x - 9 ≥ 15 + 12x, x ∈ R }. Find the range of set A ∩ B and represent it on a number line. Linear Inequations, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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