Five years from now, Sunil will be 1 1 2 times his present age. How old is he now?

Let, present age of Sunil is x years. After 5 years, age of Sunil will be x + 5 years. According to question, x + 5 = x × 1 1 2 ⇒ x + 5 = x × 3 2 ⇒ 2 x + 5 = 3 x ⇒ 2 x + 10 = 3 x ⇒ 3 x - 2 x = 10 ⇒ x = 10 So, Sunil is 10 years now.

Solve the following inequation: 3 3 p + 8 ≥ - 15 , x ∈ W

Given inequation: 3 3 p + 8 ≥ - 15 , x ∈ W Now, 3 3 p + 8 ≥ - 15 ⇒ 3 3 p + 8 3 ≥ - 15 3 Dividing both sides by 3 ⇒ 3 p + 8 ≥ - 5 ⇒ 3 p + 8 - 8 ≥ - 5 - 8 Subtracting 8 from both sides ⇒ 3 p ≥ - 13 ⇒ 3 p 3 ≥ - 13 3 ⇒ p ≥ - 13 3 As solution of p is a set of whole numbers; the solution set for p is 0 , 1 , 2 , 3 , 4 . . . . .

Solve the following inequation. 2 d - 3 + 4 d ≥ 3 , d ∈ W

We have 2 d - 3 + 4 d ≥ 3 The set of values of the variables which satisfy the given inequation, i.e. which makes the inequality a true statement is called its solution. 2 d - 3 + 4 d ≥ 3 2 d - 6 + 4 d ≥ 3 6 d - 6 ≥ 3 An inequation remains changed if the same number is added to both of its sides. Adding 6 to both sides, we get, 6 d ≥ 9 An inequation remains changed if both of its sides are divided by the same positive number. Dividing both sides by 6 , we get d ≥ 1 . 5 As d ∈ W , therefore the solution set of the equation is 2 , 3 , 4 , 5 , . . . . .