# Class 11 RD Sharma Solutions – Chapter 15 Linear Inequations – Exercise 15.1 | Set 2

### Question 15. Solve:<âˆ’ 5 in R.

Solution:

Given:<âˆ’ 5

â‡’ <

â‡’ 6(5âˆ’2x) < 3(xâˆ’30)

â‡’ 30 âˆ’ 12x < 3x âˆ’ 90

â‡’ 15x > 120

â‡’ x > 8

Thus, the solution set is (8, âˆž).

### Question 16. Solve:â‰¥âˆ’ 3.

Solution:

Given:â‰¥âˆ’ 3.

â‡’â‰¥

â‡’ 2(4+2x) â‰¥ 3(xâˆ’60)

â‡’ 8 + 4x â‰¥ 3x âˆ’ 180

â‡’ x â‰¥ âˆ’26

Thus, the solution set is [âˆ’26, âˆž).

### Question 17. Solve:âˆ’ 2 <.

Solution:

Given:âˆ’ 2 <

â‡’<

â‡’ 2x + 3 âˆ’ 10 < 3x âˆ’ 6

â‡’ x > âˆ’1

Thus, the solution set is (âˆ’1, âˆž).

### Question 18. Solve: xâˆ’2 â‰¤

Solution:

Given: xâˆ’2 â‰¤

â‡’ 3(xâˆ’2) â‰¤ 5x+8

â‡’ 3x âˆ’ 6 â‰¤ 5x + 8

â‡’ 2x â‰¥ âˆ’14

â‡’ x â‰¥ âˆ’7

Thus, the solution set is [âˆ’7, âˆž).

### Question 19. Solve:< 0.

Solution:

Given:< 0.

Case I: When 6x âˆ’ 5 > 0 and 4x +1 < 0

â‡’ x > 5/6 and x < âˆ’1/4, which is clearly impossible.

Case II: When 6x âˆ’ 5 < 0 and 4x +1 > 0

â‡’ x < 5/6 and x > âˆ’1/4

Thus, the solution set is (âˆ’1/4, 5/6).

### Question 20. Solve:> 0.

Solution:

Given:> 0.

Case I: When 2xâˆ’3 > 0 and 3xâˆ’7 > 0

â‡’ x > 3/2 and x > 7/3

â‡’ x > 7/3 ….(a)

Case II: When 2xâˆ’3 < 0 and 3xâˆ’7 < 0

â‡’ x < 3/2 and x < 7/3

â‡’ x < 3/2 ….(b)

From (a) and (b), we get:

The solution set is (âˆ’ âˆž, 3/2)âˆª (7/3, âˆž).

### Question 21. Solve:< 1.

Solution:

Given:< 1

â‡’âˆ’1 < 0

â‡’< 0

â‡’> 0

Case I: When xâˆ’5 > 0 and xâˆ’2 > 0

â‡’ x > 5 and x > 2

â‡’ x > 5 ….(a)

Case II: When xâˆ’5 < 0 and xâˆ’2 < 0

â‡’ x < 5 and x < 2

â‡’ x < 2 ….(b)

From (a) and (b), we get:

The solution set is (âˆ’ âˆž, 2)âˆª (5, âˆž).

### Question 22. Solve:â‰¤ 2.

Solution:

Given:â‰¤ 2

â‡’âˆ’ 2 â‰¤ 0

â‡’â‰¤ 0

â‡’â‰¤ 0

Case I: When 3âˆ’2x â‰¥ 0 and xâˆ’1 < 0

â‡’ x â‰¥ 3/2 and x < 1

â‡’ x < 1 …..(a)

Case II: 3âˆ’2x â‰¤ 0 and xâˆ’1 > 0

â‡’ x â‰¥ 3/2 and x > 1

â‡’ x â‰¥ 3/2 ….(b)

From (a) and (b), we get:

The solution set is (âˆ’ âˆž, 1)âˆª (3/2, âˆž).

### Question 23. Solve:< 6

Solution:

Given:< 6

â‡’âˆ’6 < 0

â‡’< 0

â‡’< 0

Case I: When 8xâˆ’33 > 0 and 2xâˆ’5 > 0

â‡’ x > 33/8 and x > 5/2

â‡’ x > 33/8 ….(a)

Case II: When 8xâˆ’33 < 0 and 2xâˆ’5 < 0

â‡’ x < 33/8 and x <5/2

â‡’ x < 5/2 ….(b)

From (a) and (b), we get:

The solution set is (âˆ’ âˆž, 5/2)âˆª (33/8, âˆž).

### Question 24. Solve:< 1.

Solution:

Given:< 1

â‡’âˆ’ 1 < 0

â‡’< 0

â‡’< 0

Case I: When 4xâˆ’12 > 0 and x+6 < 0

â‡’ x > âˆ’3 and x < âˆ’6, which is clearly not possible.

Case II: When 4xâˆ’12 < 0 and x+6 > 0

â‡’ x < âˆ’3 and x > âˆ’6

The solution set is (âˆ’ 3, 6).

### Question 25. Solve:< 2.

Solution:

Given:< 2

â‡’âˆ’ 2 < 0

â‡’< 0

â‡’< 0

Case I: When 7x > 0 and 4âˆ’x < 0

â‡’ x > 0 and x > 4

â‡’ x > 4 ….(a)

Case II: When 7x < 0 and 4âˆ’x > 0

â‡’ x < 0 and x > 4

â‡’ x < 0 ….(b)

From (a) and (b), we get:

The solution set is (âˆ’ âˆž, 0)âˆª (4, âˆž).

### Question 26. Solve:> 2.

Solution:

Given:> 2.

â‡’âˆ’ 2 > 0

â‡’> 0

â‡’< 0

Case I: When x+7 > 0 and x+3 < 0

â‡’ x > âˆ’7 and x < âˆ’3

Case II: When x+7 < 0 and x+3 > 0

â‡’ x < âˆ’7 and x > âˆ’3, which is clearly not possible.

The solution set is (âˆ’7, âˆ’3).

### Question 27. Solve:> 4.

Solution:

Given:> 4

â‡’âˆ’ 4 > 0

â‡’> 0

â‡’> 0

â‡’< 0

Case I: When 25x+17 > 0 and 8x+3 < 0

â‡’ x > âˆ’17/25 and x < âˆ’3/8

Case II: When 25x+17 < 0 and 8x+3 > 0

â‡’ x < âˆ’17/25 and x > âˆ’3/8, which is not clearly possible.

Hence the solution set is (âˆ’17/25, âˆ’3/8).

### Question 28. Solve:> 1/2.

Solution:

Given:> 1/2.

â‡’âˆ’ 1/2 > 0

â‡’> 0

Case I: When x+5 > 0 and 2xâˆ’10 > 0

â‡’ x > âˆ’5 and x > 5

â‡’ x > 5 ….(a)

Case II: When x+5 < 0 and 2xâˆ’10 < 0

â‡’ x < âˆ’5 and x < 5

â‡’ x < âˆ’5 ….(b)

From (a) and (b), we get:

The solution set is (âˆ’ âˆž, âˆ’5)âˆª (5, âˆž).

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