Solution to Maths Chapter 1 Exercise 1.1

Question 1: Convert the following statements into equations:
(a) 4 added to thrice a number is 22
(b) One-third of a number diminished by 5 is 7.

Solution:
(a) Let the number be x. According to the statement, "4 added to thrice a number is 22", we can write the equation as:
3x + 4 = 22

(b) Let the number be y. According to the statement, "One-third of a number diminished by 5 is 7", we can write the equation as:
(y/3) - 5 = 7

Question 2: Solve the following equations:
(a) 2x + 5 = 17
(b) 3y - 7 = 8

Solution:
(a) To solve the equation 2x + 5 = 17, we need to isolate x on one side of the equation. We can do so by subtracting 5 from both sides of the equation:
2x + 5 - 5 = 17 - 5
2x = 12
x = 6

(b) To solve the equation 3y - 7 = 8, we need to isolate y on one side of the equation. We can do so by adding 7 to both sides of the equation:
3y - 7 + 7 = 8 + 7
3y = 15
y = 5

Question 3: Verify whether x = -2 is a solution of the equation 3x + 4 = 10.

Solution:
To verify whether x = -2 is a solution of the equation 3x + 4 = 10, we substitute x = -2 in the equation and check if it satisfies the equation:
3(-2) + 4 = 10
-6 + 4 = 10
-2 = 10 (not true)

As -2 is not equal to 10, x = -2 is not a solution of the equation 3x + 4 = 10.