The smallest value of x which satisfies the inequation

by

Given: P {x : 5 < 2x – 1 ≤ 11, x∈R)
Q{x : – 1 ≤ 3 + 4x < 23, x∈I) where
R = (real numbers), I = (integers)
Represent P and Q on number line. Write down the elements of P ∩ Q. (1996)

Solution:

P= {x : 5 < 2x – 1 ≤ 11}
5 < 2x – 1 ≤ 11

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Ex 4 Q35.1

If x ∈ I, find the smallest value of x which satisfies the inequation 2x+\frac { 5 }{ 2 } >\frac { 5x }{ 3 } +2

Solution:

2x+\frac { 5 }{ 2 } >\frac { 5x }{ 3 } +2
⇒ 2x-\frac { 5x }{ 3 } >2-\frac { 5 }{ 2 }
⇒ 12x – 10x > 12 – 15
⇒ 2x > – 3
⇒ x>-\frac { 3 }{ 2 }
Smallest value of x = – 1 Ans.

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