# Solve the Following Inequation and Write the Solution Set: 13x – 5 < 15x + 4 < 7x + 12, X ε R - Mathematics

Solve the following inequation and write the solution set:

13x – 5 < 15x + 4 < 7x + 12, x ε R

Represent the solution on a real number line.

#### Solution

13x - 5 < 15x + 4 < 7x + 12, x ε R

Take 13x - 5 < 15x + 4

13x < 15x + 9

0 < 2x + 9

-9 < 2x

-9/2 < x

and

15x + 4 < 7x  + 12

15x < 7x + 8

8x < 8

x < 1

:. -9/2 < x < 1

i.e -4.5 < x < 1

∴ Solution set = {x : -4.5  < x < 1, x ∈ R}

The solution on the number line is as follows:

Concept: Representation of Solution on the Number Line
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