RD Chapter 15 Linear Inequations Ex 15.1 Solutions
Question - 11 : - [2(x-1)]/5 ≤ [3(2+x)]/7
Answer - 11 : -
Given:
[2(x-1)]/5 ≤ [3(2+x)]/7
(2x – 2)/5 ≤ (6 + 3x)/7
Multiply both the sides by 5 we get,
(2x – 2)/5 × 5 ≤ (6 + 3x)/7 × 5
2x – 2 ≤ 5(6 + 3x)/7
7 (2x – 2) ≤ 5 (6 + 3x)
14x – 14 ≤ 30 + 15x
14x – 14 + 14 ≤ 30 + 15x + 14
14x ≤ 44 + 15x
14x – 44 ≤ 44 + 15x – 44
14x – 44 ≤ 15x
15x ≥ 14x – 44
15x – 14x ≥ 14x – 44 – 14x
x ≥ –44
∴ The solution of the given inequation is [–44, ∞).
Question - 12 : - 5x/2 + 3x/4 ≥ 39/4
Answer - 12 : -
Given:
5x/2 + 3x/4 ≥ 39/4
By taking LCM
[2(5x)+3x]/4 ≥ 39/4
13x/4 ≥ 39/4
Multiply both the sides by 4 we get,
13x/4 × 4 ≥ 39/4 × 4
13x ≥ 39
Divide both sides by 13, we get
13x/13 ≥ 39/13
x ≥ 39/13
x ≥ 3
∴ The solution of the given inequation is [3, ∞).
Question - 13 : - (x – 1)/3 + 4 < (x – 5)/5 – 2
Answer - 13 : -
Given:
(x – 1)/3 + 4 < (x – 5)/5 – 2
Subtract both sides by 4 we get,
(x – 1)/3 + 4 – 4 < (x – 5)/5 – 2 – 4
(x – 1)/3 < (x – 5)/5 – 6
(x – 1)/3 < (x – 5 – 30)/5
(x – 1)/3 < (x – 35)/5
Cross multiply we get,
5 (x – 1) < 3 (x – 35)
5x – 5 < 3x – 105
5x – 5 + 5 < 3x – 105 + 5
5x < 3x – 100
5x – 3x < 3x – 100 – 3x
2x < –100
Divide both sides by 2, we get
2x/2 < -100/2
x < -50
∴ The solution of the given inequation is (-∞, -50).
Question - 14 : - (2x + 3)/4 – 3 < (x – 4)/3 – 2
Answer - 14 : -
Given:
(2x + 3)/4 – 3 < (x – 4)/3 – 2
Add 3 on both sides we get,
(2x + 3)/4 – 3 + 3 < (x – 4)/3 – 2 + 3
(2x + 3)/4 < (x – 4)/3 + 1
(2x + 3)/4 < (x – 4 + 3)/3
(2x + 3)/4 < (x – 1)/3
Cross multiply we get,
3 (2x + 3) < 4 (x – 1)
6x + 9 < 4x – 4
6x + 9 – 9 < 4x – 4 – 9
6x < 4x – 13
6x – 4x < 4x – 13 – 4x
2x < –13
Divide both sides by 2, we get
2x/2 < -13/2
x < -13/2
∴ The solution of the given inequation is (-∞, -13/2).