Page 161 - ICSE Math 7

Example 5: Solve the inequation 4(x – 5) > 3x – 25, x ∈{–4, –5, 0, 4} and represent the solution
set graphically.

Solution: 4(x – 5) > 3x – 25
⇒ 4x – 20 > 3x – 25

⇒ 4x – 3x > –25 + 20

⇒ x > –5
So, the possible values of x from the replacement set are –4, 0 and 4.

\ Solution set = {–4, 0, 4}
To represent the solution set graphically, draw a number line and mark –4, 0 and 4 by
thick dots.

–5 –4 –3 –2 –1 0 1 2 3 4

Example 6: If a labour earns ` 800 per day, how many labourers can work within a monthly budget
of ` 1,44,000?
Solution: Let the number of labourers be x.

Then, wages earned by x labourers per day = ` 800 x
Wages that x labourers will earn per month = ` (800 x × 30) = ` 24,000 x
But, as per the given condition this amount cannot exceed ` 1,44,000.
Therefore, 24,000 x ≤ 1,44,000
24,000 x 1,44,000
≤
24,000 24,000
x ≤ 6
Hence up to 6 labourers can work in a monthly budget of ` 1,44,000.

EXERCISE

1. Solve the following inequations.

(a) x + 4 > 2, x ∈ Z (b) 3x + 3 < 12, x ∈ N (c) 3(x + 2) ≤ 24 + x, x ∈ W
x x
(d) 2x + 9 ≥ 3x – 5, x ∈ {10, 11, 12, 13, 14, 15} (e) – 1 ≥ – 2, x ∈ W
3 2
2. Find the solution set of the following, if the replacement set is {0, 1, 2, 3, 4, 5}.

(a) 3 – 2x < 6 (b) x + 2 ≤ 5 (c) 5(x + 7) ≥ 35 – x

5x – 1 2x 1 x 1
(d) ≥ 3 (e) – ≥ + (f) 6(2 – x) ≥ 4(x – 8)
3 3 4 5 2
3. Solve the following inequations and represent the solution set graphically.
(a) x + 6 > 12, x ∈ Z (b) 13x – 19 ≥ 7, x ∈ N

(c) 8x + 1 ≤ 4x + 5, x ∈ W (d) 7(x + 1) < 5x + 10, x ∈ W
4. Ria needs at least 5 packets of pencils having 15 pencils each. If one pencil costs ` 8 and Ria has
only ` 600, how many packets of pencils can she buy?

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