Solve the following inequation and write the solution set

Q) Solve the following inequation and write the solution set: 13x – 5 < 15 x + 4 < 7 x + 12, X∈R

Ans:

Step 1: Let’s take first 2 entries:

13x – 5 < 15 x + 4

∴ 13 x < 15 x + 4 + 5

∴ 0 < 2 x + 9

∴ – 9 < 2 x

∴ x > $\frac{- 9}{2}$

Step 2: Next, we take last 2 entries:

15 x + 4 < 7 x + 12

∴ 15 x < 7 x + 12 – 4

∴ 15 x – 7 x < 8

∴ 8 x < 8

∴ x < 1

∴ $\frac{- 9}{2}$ < x < 1

∴ – 4.5 < x < 1

Therefore, the solution set is (- 4.5,1)

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