Chapter 15: Linear Inequations – Exercise 15.2
Linear Inequations – Exercise – 15.2 – Q.1
Consider the first inequation,
x + 3 > 0
x > - 3 .... (i)
Consider the second inequation,
2x < 14
x < 14/2 = 7
x < 7 …. (ii)
From (i) and (ii), (- 3, 7) is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.2
Consider the first inequation,
2x – 7 > 5 - x
⟹ 2x + x > 5 + 7
⟹ 3x > 12
⟹ x >12/3
⟹ x > 4 …….. (i)
Consider the second inequation,
11 - 5x ≤ 1
⟹ - 5x ≤ 1 - 11
⟹ - 5x ≤ - 10
⟹ 5x ≥ 10
⟹ x ≥ 2 …….. (ii)
From (i) and (ii), (4, ∞) is the solution set of the simultaneous equtions.
Linear Inequations – Exercise – 15.2 – Q.3
Consider the first inequation,
x - 2 > 0
x > 2 .... (i)
Consider the second inequation,
3x < 18
x < 6 ....... (ii)
From (i) and (ii), (2, 6) is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.4
Consider the first inequation,
2x + 6 ≥ 0
2x ≥ - 6
x ≥ (-6)/2
x ≥ - 3 …….. (i)
consider the second inequation,
4x – 7 < 0
4x < 7
x < 7/4 ……. (ii)
From (i) and (ii), [- 3, 7/4] is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.5
Consider the first inequation,
3x – 6 > 0
3x > 6
x > 2 …….. (i)
Consider the second inequation,
2x – 5 > 0
2x > 5
x > 5/2 …. (ii)
From (i) and (ii), [5/2, ∞] is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.6
Consider the first inequation,
2x – 3 < 7
2x < 7 + 3
2x < 10
x < 5 ….. (i)
Consider the second inequation,
2x > - 4
x > (-4)/2
x > - 2 ….. (ii)
From (i) and (ii), [-2, 5] is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.7
Consider the first inequation,
2x + 5 ≤ 0
2x ≤ - 5
x ≤ (-5)/2 …… (i)
Consider the second inequation,
x – 3 ≤ 0
x ≤ 3 …… (ii)
From (i) and (ii), (-∞, – 5/2] is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.8
5x – 1 < 24
5x < 24 + 1
5x < 25
x < 25/5
x < 5 …… (1)
and
5x + 1 > - 24
5x > - 24 - 1
5x > - 25
x > - 5 .…. (2)
From equation (1) and (2),
< x < 5
⟹ (- 5, 5)
Linear Inequations – Exercise – 15.2 – Q.9
Consider the first inequation,
3x - 1 ≥ 5
3x ≥ 5 + 1
3x ≥ 6
x ≥ 2 ..... (i)
Consider the second inequatin,
x + 2 > -1
x > -1 -2
x > -3 ...... (ii)
From (i) and (ii), [2, ∞] is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.10
Consider the first inequation,
11 - 5x > -4
-5x > -4 - 11
-5x < -15
5x < 15
x < 3 .... (i)
Consider the second inequation,
4x + 13 ≤ -11
4x ≤ -11 - 13
4x ≤ -24
x ≤ -6 ...(ii)
From (i) and (ii), [-∞,-6] is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.11
Consider the first inequation,
4x – 1 ≤ 0
4x > - 1
- 5x ≤ - 15
x ≤ 1/4 ….. (i)
Consider the second inequation,
3 - 4x < 0
- 4x < - 3
- x <- 3/4
x > 3/4 …… (ii)
From (i) and (ii), there is no solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.12
Consider the first inequation,
x + 5 > 2(x + 1)
x > 2x + 2 - 5
x > 2x - 3
x - 2 > - 3
-x > - 3
x < 3 ...... (i)
Consider the second inequation,
2 - x < 3(x + 2)
2 - x < 3x + 6
-x - 3x < 6 - 2
- 4x < 4
x > -1 ..... (ii)
From (i) and (ii), (-1, 3) is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.13
Consider the first inequation,
2(x - 6) < 3x - 7
⟹ 2x - 12 < 3x - 7
⟹ - 5 < x ...... (i)
Consider the second inequation,
11 - 2x < 6 - x
-2x + x < 6 - 11
- x < - 5
x > 5 ....... (ii)
From (i) and (ii), (5, ∞) is the solution set of the simultaneous equations.
Linear Inequations – Exercise – 15.2 – Q.14
Consider the first inequation,
5x – 7 < 3(x + 3)
5x - 7< 3x + 9
5x - 3x < 9 + 7
2x < 16
x < 8 ……. (i)
Consider the second inequation,
From (i) and (ii), (-∞, 2) is the solution set of the simultaneous equations.