## 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**

Sol :

Adding 1 to both sides of the given equation, we obtain

x – 1 + 1 = 0 + 1

x = 1

**(b) x + 1 = 0**

Sol :

Subtracting 1 from both sides of the given equation , we obtain

x + 1 – 1 = 0 – 1

x = – 1

**(c) x – 1 = 5**

Sol :

Adding 1 to both sides of the given equation, we obtain

x – 1 + 1 = 5 + 1

x = 6

**(d) x + 6 = 2**

Sol :

Subtracting 6 from both sides of the given equation, we obtain

x + 6 – 6 = 2 – 6

x = – 4

**(e) y – 4 = -7**

Sol :

adding 4 to both sides of the given equation , we obtain

y – 4 + 4= -7 + 4

y = -3

**(f) y – 4 = 4**

Sol :

Adding 4 to both sides of the given equation, we obtain

y – 4 + 4 = 4 + 4

y = 8

**(g) y + 4 = 4**

Sol :

Subtracting 4 from both sides of the given equation , we obtain

y + 4 – 4 = 4 – 4

y = 0

**(h) y + 4 = -4**

Sol :

Subtracting 4 from both sides of the given equation , we obtain

y + 4 – 4 = 4 – 4

y = -8

QUESTION 2

**Give the first step you will use to separate the variable and then solve the equation:**

**(a) 3 l = 42**

Sol :

Dividing both sides of the given equation by 3, we obtain

*l* = 14

**(b)**

Sol :

Multiplying both sides of the given equation by 2, we obtain

*b* = 12

**(c)**

Sol :

Multiplying both sides of the given equation by 7, we obtain

*p* = 28

**(d) 4x = 25**

Sol :

Dividing both sides of the given equation by 4, we obtain

**(e) 8y = 36**

Sol :

Dividing both sides of the given equation by 8, we obtain

**(f)**

Sol :

Multiplying both sides of the given equation by 3, we obtain

**(g)**

Sol :

Multiplying both sides of the given equation by 5, we obtain

**(h) 20t = -10**

Sol :

Dividing both sides of the given equation by 20, we obtain

QUESTION 3

**Give the steps you will use to separate the variable and then solve the equation:**

**(a) 3n – 2 = 26**

Sol :

Adding 2 to both sides of the given equation, we obtain

3n – 2 + 2 = 46 + 2

3n = 48

Dividing both sides of the given equation by 3, we obtain

*n* = 16

**(b) 5m + 7 = 7**

Sol :

Subtracting 7 from both sides of the given equation, we obtain

5m + 7 – 7 = 17 – 7

5m = 10

Dividing both sides of the given equation by 5, we obtain

*m* = 2

**(c)**

Sol :

Multiplying both sides of the given equation by 3, we obtain

20p = 120

Dividing both sides of the given equation by 20, we obtain

*p* = 6

**(d)**

Sol :

Multiplying both sides of the given equation by 10, we obtain

3p = 60

Dividing both sides of the given equation by 3, we obtain

*p* = 20

QUESTION 4

**Solve the following equations:**

**(a) 10p = 100**

Sol :

*p* = 10

**(b) 10p + 10**

Sol :

10p + 10 – 10 = 100 – 10

10 p = 90

*p* = 9

**(c)**

Sol :

*p* = 20

**(d)**

Sol :

*p* = -15

**(e)**

Sol :

3p = 24

*p* = 8

**(f) 3s = -9**

Sol :

*x* = -3

**(g) 3s + 12 = 0**

Sol :

3s + 12 -12 = 0 -12

3s = -12

s = -4

**(h) 3s = 0**

Sol :

s = 0

**(i) 2q = 6**

Sol :

q = 3

**(j) 2q – 6 = 0**

Sol :

2q – 6 + 6 = 0 + 6

2q = 6

*q* = 3

**(k) 2q + 6 = 0**

Sol :

2q + 6 – 6 = 0

2q = -6

*q* = -3

**(l) 2q + 6 = 12**

Sol :

2q + 6 – 6 = 12 – 6

2q = 6

*q* = 3