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 - Noon Academy

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

Class 10 | Exercise 1 | ICSE | Linear Inequations | Maths | ML Aggarwal

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

According to ques,

$~A\text{ }=\text{ }\{x\text{ }:\text{ }11x\text{ }\text{ }5\text{ }>\text{ }7x\text{ }+\text{ }3,\text{ }x\in R\}$

and

$B\text{ }=\text{ }\{x\text{ }:\text{ }18x\text{ }\text{ }9\text{ }\ge \text{ }15\text{ }+\text{ }12x,\text{ }x\in R\}$

Solving for A,

$11x\text{ }\text{ }5\text{ }>\text{ }7x\text{ }+\text{ }3$

$11x\text{ }\text{ }7x\text{ }>\text{ }3\text{ }+\text{ }5$

$4x\text{ }>\text{ }8$

$x\text{ }>\text{ }2$

Hence,

$~A\text{ }=\text{ }\{x\text{ }:\text{ }x\text{ }>\text{ }2,\text{ }x\in R\}$

Next, solving for B

$18x\text{ }\text{ }9\text{ }\ge \text{ }15\text{ }+\text{ }12x$

$18x\text{ }\text{ }12x\text{ }\ge \text{ }15\text{ }+\text{ }9$

$6x\text{ }\ge \text{ }24$

$x\text{ }\ge \text{ }4$

Hence,

$B\text{ }=\text{ }\{x\text{ }:\text{ }x\text{ }\ge \text{ }4,\text{ }x\in R\}$

Hence,

$A\text{ }\cap \text{ }B\text{ }=\text{ }x\text{ }\ge \text{ }4$

Representing the solution on a number line:

ML Aggarawal Solutions for Class 10 Chapter 4 - 23

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