Chapter 15: Linear Inequations – Exercise 15.1

3x + 9≥ - x + 19

⟹ 3x + x ≥ 19 - 9

⟹ 4x ≥ 10

Linear Inequations – Exercise – 15.1 – Q.7

Linear Inequations – Exercise – 15.1 – Q.8

Linear Inequations – Exercise – 15.1 – Q.9

- (x - 3) + 4 < 5 - 2x

⟹ -x + 3 + 4 < 5 - 2x

⟹ -x + 7 < 5 - 2x

⟹ -x + 2x < 5 - 7

⟹ x < – 2

(- ∞, - 2) is the solution set

Linear Inequations – Exercise – 15.1 – Q.10

Linear Inequations – Exercise – 15.1 – Q.11

⟹ 7(2(x - 1)) ≤ 5(3(2 + x))

⟹ 14(x - 1) ≤ 15(2 + x)

⟹ 14x – 14 ≤ 30 + 15x

⟹ 14x – 15 x ≤ 30 + 14

⟹- x ≤ 44

⟹ x ≥ - 44

∴ The solution set is [- 44, ∞)

Linear Inequations – Exercise – 15.1 – Q.12

⟹ x ≥ 3

∴ The solution set is [3, ∞)

Linear Inequations – Exercise – 15.1 – Q.13

5(x – 1 + 12) < 3(x – 5 - 10)

5(x + 11) < 3(x - 15)

5x + 55 < 3x - 45

5x - 3x < - 45 - 55

2x < - 100

x < - 50

∴ The solution set is (-∞, - 50)

Linear Inequations – Exercise – 15.1 – Q.14

3(2x + 3 - 12) <4 (x – 4 - 6)

3(2x - 9) <4 (x - 10)

6x – 27 < 4x - 40

6x - 4x < - 40 + 27

2x < - 13

Linear Inequations – Exercise – 15.1 – Q.15

6(5 - 2x) <3 (x - 30)

30 – 12 x < 3x - 90

- 12x - 3x < - 90 - 30

- 15x < - 120

15x < - 120

x > 120/15 = 8

∴ The solution set is (8, ∞)

Linear Inequations – Exercise – 15.1 – Q.16

2(4 + 2x) ≥ 3(x - 6)

8 + 4 x ≥ 3x - 18

4x - 3x ≥ - 18 - 8

X ≥ - 26

∴ The solution set is [- 26, ∞)

Linear Inequations – Exercise – 15.1 – Q.17