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• RD Sharma Class 11 Solutions for Maths

# Class 11 RD Sharma Solutions- Chapter 15 Linear Inequations – Exercise 15.2 | Set 1

### Question 1. Solve each of the following system of equations in R: x + 3 > 0, 2x < 14

Solution:

Let the first equation be x+3>0

â‡’ x > -3

and the second equation be 2x < 14

â‡’ x < 7

Hence, using above equations, we know x lies in range (-3,7)

### Question 2. Solve each of the following system of equations in R: 2x – 7 > 5 – x, 11 – 5x â‰¤ 1

Solution:

Let the first equation be 2x – 7 > 5 – x

â‡’ 3x > 12

â‡’ x >4

and the second equation be 11 – 5x â‰¤ 1

â‡’ 10 â‰¤ 5x

â‡’ 2 â‰¤ x

Hence, using above equations, we know x lies in range (4,âˆž)

### Question 3. Solve each of the following system of equations in R: x – 2 > 0, 3x < 18

Solution:

Let the first equation be x – 2 > 0

â‡’ x > 2

and the second equation be 3x < 18

â‡’ x < 6

Hence, using above equations, we know x lies in range (2,6)

### Question 4. Solve each of the following system of equations in R: 2x + 6 â‰¥ 0, 4x – 7 < 0

Solution:

Let the first equation be 2x+6 â‰¥ 0

â‡’ 2x â‰¥ -6

â‡’ x â‰¥ -3

and the second equation be 4x – 7< 0

â‡’ 4x < 7

â‡’ x < 7/4

Hence, using above equations, we know x lies in range [-3, 7/4)

### Question 5. Solve each of the following system of equations in R: 3x – 6 > 0, 2x – 5 >0

Solution:

Let the first equation be 3x – 6 > 0

â‡’ 3x > 6

â‡’ x > 2

and the second equation be 2x – 5> 0

â‡’ 2x > 5

â‡’ x > 5/2

Hence, using above equations, we know x lies in range (5/2, âˆž)

### Question 6. Solve each of the following system of equations in R: 2x – 3 < 7, 2x > -4

Solution:

Let the first equation be 2x – 3 < 7

â‡’ 2x < 10

â‡’ x < 5

and the second equation be 2x > – 4

â‡’ x > -2

Hence, using above equations, we know x lies in range (-2, 5)

### Question 7. Solve each of the following system of equations in R: 2x + 5 â‰¤ 0, x – 3 â‰¤ 0

Solution:

Let the first equation be 2x + 5 â‰¤ 0

â‡’ 2x â‰¤ -5

â‡’ x â‰¤ -5/2

and the second equation be x – 3 â‰¤ 0

â‡’ x â‰¤ 3

Hence, using above equations, we know x lies in range (-âˆž, -5/2]

### Question 8. Solve each of the following system of equations in R: 5x – 1 < 24, 5x + 1 > -24

Solution:

Let the first equation be 5x – 1 < 24

â‡’ 5x < 25

â‡’ 5x < 25

â‡’ x < 5

and the second equation be 5x + 1 > -24

â‡’ 5x > -25

â‡’ x > -5

Hence, using above equations, we know x lies in range (-5, -5)

### Question 9. Solve each of the following system of equations in R: 3x – 1 â‰¥ 5, x + 2 > -1

Solution:

Let the first equation be 3x – 1 â‰¥ 5

â‡’ 3x â‰¥ 6

â‡’ x â‰¥ 2

and the second equation be x + 2 > -1

â‡’ x > -3

Hence, using above equations, we know x lies in range [2, âˆž)

### Question 10. Solve each of the following system of equations in R: 11 – 5x > -4, 4x + 13 â‰¤ -11

Solution:

Let the first equation be 11 – 5x > -4

â‡’ 15 > 5x

â‡’ x < 3

and the second equation be 4x + 13 â‰¤ -11

â‡’ 4x â‰¤ -24

â‡’ x â‰¤ -6

Hence, using above equations, we know x lies in range (-âˆž, -6]

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