Represent the solution set on the number line.

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Solve the inequation 2x – 5 ≤ 5x + 4 < 11, where x ∈ I. Also represent the solution set on the number line. (2011)

Solution:

2x – 5 ≤ 5x + 4 < 11 2x – 5 ≤ 5x + 4
⇒ 2x – 5 – 4 ≤ 5x and 5x + 4 < 11
⇒ 2x – 9 ≤ 5x and 5x < 11 – 4
and 5x < 7
⇒ 2x – 5x ≤ 9 and x < \\ \frac { 7 }{ 5 }
⇒ 3x > – 9 and x< 1.4
⇒ x > – 3
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Ex 4 Q31.1

If x ∈ I, A is the solution set of 2 (x – 1) < 3 x – 1 and B is the solution set of 4x – 3 ≤ 8 + x, find A ∩B.

Solution:

2 (x – 1) < 3 x – 1
2x – 2 < 3x – 1
2x – 3x < – 1 + 2 ⇒ – x < 1 x > – 1
Solution set A = {0, 1, 2, 3, ..,.}
4x – 3 ≤ 8 + x
4x – x ≤ 8 + 3
⇒ 3x ≤ 11
⇒ x ≤ \\ \frac { 11 }{ 3 }
Solution set B = {3, 2, 1, 0, – 1…}
A ∩ B = {0, 1, 2, 3} Ans.

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