Page 15 - mathsvol1ch1to3ans

15

1 1 3 1 1 3
x − < − x + OR x − < x −
4 2 4 4 2 4
3 1 1
x < 1 OR x < −
2 2 2
2
x < OR x < −1
3
The solution set is {−∞, −1}

1
2. Solve < 6 and express the solution using the interval notation.
|2x − 1|
1
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Solution: Given |2x − 1| >
6
1 1
(2x − 1) > OR (2x − 1) < −
6 6
7 5
2x > OR 2x <
6 6
7 5
x > OR x <
12 12

5 7
x ∈ −∞, ∪ , ∞
12 12
3. Solve −3|x| + 5 ≤ −2 and graph the solution set in a number line.
Solution:
−3|x| ≤ −7

7
|x| ≥
3
7 7
x ≥ OR x ≤ −
3 3

7 7
x ∈ −∞, − OR x ∈ , ∞
3 3
4. Solve 2|x + 1| − 6 ≤ 7 and graph the solution set in a number line.
Solution:
13
|x + 1| ≤
2
13 13
(x + 1) ≤ (or) (x + 1) ≥ −
2 2
11 15
x ≤ (or) x ≥ −
2 2

15 11
x ∈ − ,
2 2
1
5. Solve |10x − 2| < 1.
5
Solution:
|10x − 2| < 5