Page 16 - mathsvol1ch1to3ans

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(10x − 2) < 5 (or) (10x − 2) > −5

7 3
x < (or) x > −
10 10

3 7
x ∈ − ,
10 10
6. Solve |5x − 12| < −2.
Solution:
(5x − 12) < −2 (or) (5x − 12) > 2
14
x < 2 (or) x >
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5

14
x ∈ (−∞, 2) ∪ , ∞ ⇒ x ∈ ∅
5
Hence No solution
1 1
7. Solve < .
|x| − 3 2
Solution:
|x| − 3 > 2 ⇒ |x| > 5

x > 5(or)x < −5

x ∈ (−∞, −5) ∪ (5, ∞)

Exercise - 2.8

1. Represent the following inequalities in the interval notation:
(i) x ≥ −1 and x < 4 x ∈ [−1, 4)

(ii) x ≤ 5 and x ≥ −3 x ∈ [−3, 5]
(iii) x < −1 or x < 3 x ∈ (−∞, 3)

(iv) −2x > 0 or 3x − 4 < 11 x ∈ (−∞, 5)

2. Solve 23x < 100 when
(i) x is a natural number {1, 2, 3, 4}

(ii) x is an integer. {. . . , −3, −2, −1, 0, 1, 2, 3, 4}
3. Solve −2x ≥ 9 when
9
(i) x is a real number (−∞, − ]
2
(ii) x is an integer (. . . , −7, −6, −5]
(iii) x is a natural number. {}