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

⇒ x > -3

and the second equation be 2x < 14

⇒ 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 ≤ 1

Solution:

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

⇒ 3x > 12

⇒ x >4

and the second equation be 11 - 5x ≤ 1

⇒ 10 ≤ 5x

⇒ 2 ≤ x

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

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

⇒ x > 2

and the second equation be 3x < 18

⇒ 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 ≥ 0, 4x - 7 < 0

Solution:

Let the first equation be 2x+6 ≥ 0

⇒ 2x ≥ -6

⇒ x ≥ -3

and the second equation be 4x - 7< 0

⇒ 4x < 7

⇒ 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

⇒ 3x > 6

⇒ x > 2

and the second equation be 2x - 5> 0

⇒ 2x > 5

⇒ x > 5/2

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

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

⇒ 2x < 10

⇒ x < 5

and the second equation be 2x > - 4

⇒ 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 ≤ 0, x - 3 ≤ 0

Solution:

Let the first equation be 2x + 5 ≤ 0

⇒ 2x ≤ -5

⇒ x ≤ -5/2

and the second equation be x - 3 ≤ 0

⇒ x ≤ 3

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

⇒ 5x < 25

⇒ 5x < 25

⇒ x < 5

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

⇒ 5x > -25

⇒ 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 ≥ 5, x + 2 > -1

Solution:

Let the first equation be 3x - 1 ≥ 5

⇒ 3x ≥ 6

⇒ x ≥ 2

and the second equation be x + 2 > -1

⇒ x > -3

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

Question 10. Solve each of the following system of equations in R: 11 - 5x > -4, 4x + 13 ≤ -11

Solution:

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

⇒ 15 > 5x

⇒ x < 3

and the second equation be 4x + 13 ≤ -11

⇒ 4x ≤ -24

⇒ x ≤ -6

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