Solve the following inequation. 2 a + 3 ≤ 13 , where a is a whole number.

Given, 2 a + 3 ≤ 13 , where a is a whole number. Subtracting 3 from both the sides, we get 2 a + 3 - 3 ≤ 13 - 3 ⇒ 2 a ≤ 10 Dividing both the side by 2 , we get 2 a 2 ≤ 10 2 ⇒ a ≤ 5 So, a is a whole number less than or equal to 5 . Whole numbers less than 5 are 0 , 1 , 2 , 3 and 4 . Hence, the required values of a are 0 , 1 , 2 , 3 , 4 and 5 .

Solve the following inequation. 6 x - 7 ≥ 35 , where x is an integer.

Given: 6 x - 7 ≥ 35 , where x is an integer. Adding 7 to both the sides, we get 6 x - 7 + 7 ≥ 35 + 7 ⇒ 6 x ≥ 42 Dividing both the sides by 6 , we get 6 x 6 ≥ 42 6 ⇒ x ≥ 7 So, x is an integer greater than or equal to 7 . We know the set of integers, Z = . . . . . . . . . , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , . . . . . . . . . . . Thus, the integers greater than and equal to 7 are 7 , 8 , 9 , 10 , . . . . … . Hence, the values of x are 7 , 8 , 9 , 10 , . . . . … .

Solve the inequation - 7 ≤ y , y is a negative integer, and represent the solution on the number line.

Given: - 7 ≤ y , y is a negative integer. We know that the set of integers, Z = . . . . . . . . . , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , . . . . . . . . - 7 ≤ y ⇒ y ≥ - 7 So, y is a negative integer greater than or equal to - 7 . So, the negative integers greater than or equal to - 7 are - 7 , - 6 , - 5 , - 4 , - 3 , - 2 , - 1 . On the number line the red points marked represents the solution - 7 , - 6 , - 5 , - 4 , - 3 , - 2 , - 1 .