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ICSE Class X Math 2015 Paper

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Question : 3 of 52
Marks: +1, -0
Solve the following inequation and write the solution set :
13x−5<15x+4<7x+12,x∈R13x-5 < 15x+4 < 7x+12, x\in \mathbb{R}
Represent the solution on a real number line.
Solution:  
Given:     13x−5<15x+4<7x+12\;\; 13x-5 < 15x+4 < 7x+12
⇒15x+4>13x−5     and     15x+4<7x+12\Rightarrow 15x+4 > 13x-5 \;\; \text{ and } \;\; 15x+4 < 7x+12
⇒15x−13x>−5−4\Rightarrow 15x-13x > -5-4
⇒2x>−9\Rightarrow 2x > -9
⇒x>−92     or     −4.5\Rightarrow x > \frac{-9}{2} \;\; \text{ or } \;\; -4.5
15x−7x<12−415x-7x < 12-4
8x<88x < 8
x<1x < 1
     Solution :     {x:4.5<x<1,x∈R}\;\; \text{ Solution : } \;\; \{x: 4.5 < x < 1, x \in \mathbb{R}\}
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