Solve the following inequation and write the solution set : 13 x-5< 15 x+4< 7 x+12, x\in R Represent the solution on a real number line.

ICSE Class X Math 2015 Solved Paper - Question 3

Question : 3 of 52

Marks: +1, -0

Solve the following inequation and write the solution set :

13 x-5< 15 x+4< 7 x+12, x∈ R

Represent the solution on a real number line.

Solution:

Given:

\;\; 13 x-5< 15 x+4< 7 x+12

⇒ 15 x+4>13 x-5 \;\text " and "\; 15 x+4< 7 x+12

⇒ 15 x-13 x>-5-4

⇒ 2 x>-9

⇒ x>\;{-9}/{2} \;\text " or "\;-4.5

15 x-7 x\;< 12-4

8 x\;< 8

x\;< 1

\;\text " Solution : "\;\{x: 4 . 5< x< 1, x ∈ {\R}\}

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