Chapter 15: Linear Inequations – Exercise 15.1
Linear Inequations – Exercise – 15.1 – Q.1
Now, 12x < 50
(ii) since x ϵ Z, x ϵ{…, -3, -2, -1, 0, 1, 2, 3, 4}
(iii) since x ϵ N, x ϵ {1, 2, 3, 4}
Linear Inequations – Exercise – 15.1 – Q.2
Now, - 4x > 30
As x ϵ N, so x can not be less than 1.
∴ The solution set of the inequality - 4x > 30 is null set Φ.
Linear Inequations – Exercise – 15.1 – Q.3
Now, 4x – 2 < 8
⟹ 4x < 8 + 2
⟹ 4x < 10
Linear Inequations – Exercise – 15.1 – Q.4
3x -7 > x + 1
⟹ 3x – x > 1 + 7
⟹ 2 x > 8
⟹ x > 8/2 = 4
⟹ x > 4
∴ (4, ∞) is the solution set.
Linear Inequations – Exercise – 15.1 – Q.5
x + 5 > 4x - 10
⟹ x - 4x > - 10 - 5
⟹ - 3x > - 15
⟹ 3x < 15
⟹ x < 15/3 = 5
⟹ x < 5
∴ (-∞, 5) is the solution set
Linear Inequations – Exercise – 15.1 – Q.6
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
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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
2x – 7 < 3x - 6
2x - 3x < - 6 + 7
- x < 1
X > - 1
∴ The solution set is (- 1, ∞)
Linear Inequations – Exercise – 15.1 – Q.18
3(x - 2) ≤ 5x + 8
3x – 6 ≤ 5x + 8
3x - 5x ≤ 8 + 6
- 2x ≤ 14
2x ≥ - 14
X ≥ - 7
∴ The solution set is [- 7, ∞)
Linear Inequations – Exercise – 15.1 – Q.19
Case 1: 6x – 5 > 0 and 4x + 1 < 0
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This is not possible.
Case 2: 6x – 5 < 0 and 4x + 1 > 0
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