(i) 4n + 7 ≥ 3n + 10, n is an integer.

4n + 7 – 3n ≥ 3n + 10 – 3n

n(4 – 3) + 7 ≥ 3n + 10 – 3n

n(4 – 3) + 7 ≥ n (3 – 3) + 10

n + 7 ≥ 10

Subtracting 7 on both sides

n + 7 – 7 ≥ 10 – 7

n ≥ 3

Since the solution is an integer and is greater than or equal to 3, the solution will be 3,

4, 5, 6, 7, …

n = 3, 4, 5, 6,7, …

(ii) 6(x + 6) ≥ 5(x – 3), x is a whole number.

6x + 36 ≥ 5x – 15

Subtracting 5x on both sides

6x + 36 – 5x ≥ 5x – 15 – 5x

x (6 – 5) + 36 ≥ x(5 – 5) – 15

x + 36 ≥ -15

Subtracting 36 on both sides

x + 36 – 36 ≥ -15 -36

x ≥ -51

The solution is a whole number and which is greater than or equal to -51

∴ The solution is 0, 1, 2, 3, 4,…

x = 0,1,2, 3,4,…

(iii) -13 ≤ 5x + 2 ≤ 32, x is an integer.

Subtracting throughout by 2

-13 – 2 ≤ 5x + 2 – 2 ≤ 32 – 2

-15 ≤ 5x ≤ 30

Dividing throughout by 5

\(\frac{-15}{5}\) ≤ \(\frac{5x}{5}\) ≤ \(\frac{30}{5}\)

– 3 ≤ x ≤ 6

∴ Since the solution is an integer between -3 and 6 both inclusive, we have the solution

As -3, -2, -1,0, 1,2, 3, 4, 5, 6.

i.e. x = -3, -2, 0, 1, 2, 3,4, 5 and 6.