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]