## Chapter 4 Simple Equations Exercise 4.2

Question 1: Give first the step you will use to separate the variable and then solve the equation:
(a) x – 1 = 0

Adding 1 on both the sides
= x - 1 + 1 = 0 + 1
= x = 1
So, x = 1.

(b) x + 1 = 0

Subtracting 1 on both the sides
= x + 1 - 1 = 0 - 1
= x = -1
So, x = -1.

(c) x – 1 = 5
Adding 1 on both the sides
= x - 1 + 1 = 5 + 1
= x = 6
So, x = 6.

(d) x + 6 = 2

Subtracting 6 on both the sides
= x + 6 - 6 = 2 - 6
= x = -4
So, x = -4.

(e) y – 4 = – 7

Adding 4 on both the sides
= y - 4 + 4 = -7 + 4
= y = -3
So, y = -3.

(f) y – 4 = 4

Adding 4 on both the sides
= y - 4 + 4 = 4 + 4
= y = 8
So, y = 8.

(g) y + 4 = 4

Subtracting 4 on both the sides
= y + 4 - 4 = 4 - 4
= y = 0
So, y = 4.

(h) y + 4 = – 4

Subtracting 4 on both the sides
= y + 4 - 4 = -4 - 4
= y = -8
So, y = -8.

Question 2: Give first the step you will use to separate the variable and then solve the equation:
(a) 3l = 42

Dividing 3 on both the sides
= 3l/3 = l = 42/3 = 14
So, l = 14.

(b) b/2 = 6

Multiplying 2 on both the sides
= b/2 x 2 = b = 6 x 2 = 12
So, b = 12.

(c) p/7 = 4

Multiplying 7 on both the sides
= p/7 x 7 = 4 x 7 = p = 28
So, p = 28.

(d) 4x = 25

Dividing 4 on both the sides
= 4x/4 = 25/4 = x = 25/4
So, x = 25/4.

(e) 8y = 36

Dividing 8 on both the sides
= 8y/8 = 36/8 = y = 4
So, y = 4.

(f) (z/3) = (5/4)

Multiplying 3 on both the sides
= z/3 x 3 = 5/4 x 3 = z = 15/4
So, z = 15/4.

(g) (a/5) = (7/15)

Multiplying 5 on both the sides
= a/5 x 5 = 7/15 x 5 = a = 35/15 = 7/3
So, a = 7/3.

(h) 20t = – 10

Dividing 20 on both the sides
= 20t/20 = -10/20 = t = -1/2
So, t = 1/-2.

Question 3: Give the steps you will use to separate the variable and then solve the equation:
(a) 3n – 2 = 46

Adding 2 on both the sides
= 3n - 2 + 2 = 46 + 2
= 3n = 48
Dividing 3 on both the sides
= 3n/3 = 48/3 = n = 16
So, n = 16.

(b) 5m + 7 = 17

Subtracting 7 on both the sides
= 5m + 7 - 7 = 17 - 7
= 5m = 10
Dividing 5 on both the sides
= 5m/5 = 10/5 = m = 2
So, m = 2.

(c) 20p/3 = 40

Multiplying 3 on both the sides
= 20p/3 x 3 = 40 x 3 = 20p = 120
Dividing 20 on both the sides
= 20p/20 = 120/20 = p = 60
So, p = 60.

(d) 3p/10 = 6

Multiplying 10 on both the sides
= 3p/10 x 10 = 6 x 10 = 3p = 60
Dividing 3 on both the sides
= 3p/3 = 60/3 = 20
So, p = 20.

Question 4: Solve the following equations:
(a) 10p = 100

Dividing 10 on both the sides
= 10p/10 = 100/10 = p = 10
So, p = 10.

(b) 10p + 10 = 100

Subtracting 10 on both the sides
= 10p + 10 - 10 = 100 - 10
= 10p = 90
Dividing 10 on both the sides
= 10p/10 = 90/10 = p = 9
So, p = 9.

(c) p/4 = 5

Multiplying 4 on both the sides
= p/4 x 4 = 5 x 4 = p = 20
So, p = 20.

(d) - p/3 = 5

Multiplying -3 on both the sides
= p/-3 x -3 = 5 x -3 = p = -15
So, p = -15.

(e) 3p/4 = 6

Multiplying 4 on both the sides
= 3p/4 x 4 = 6 x 4
= 3p = 24
Dividing 3 on both the sides
= 3p/3 = 24/3 = p = 8
So, p = 8.

(f) 3s = – 9

Dividing 3 on both the sides
= 3s/3 = -9/3 = s = -3
So, s = -3.

(g) 3s + 12 = 0

Subtracting 12 on both the sides
= 3s + 12 - 12 = 0 - 12
= 3s = -12
Dividing 3 on both the sides
= 3s/3 = -12/3 = s = -4
So, s = -4.

(h) 3s = 0

Dividing 3 on both the sides
= 3s/3 = 0/3 = s = 0
So, s = 0.

(i) 2q = 6

Dividing 2 on both the sides
= 2q/2 = 6/2 = q = 3
So, q = 3.

(j) 2q – 6 = 0

Adding 6 on both the sides
= 2q - 6 + 6 = 0 + 6 = 2q = 6
Dividing 2 on both the sides
= 2q/2 = 6/2 = q = 3
So, q = 3.

(k) 2q + 6 = 0

Subtracting 6 on both the sides
= 2q + 6 - 6 = 0 - 6 = 2q = -6
Dividing 2 on both the sides
= 2q/2 = -6/2 = q = -3

(l) 2q + 6 = 12