**EXERCISE 4.2**

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

**Ans:**Add 1 to both sides

x – 1 + 1 = 0 + 1

x = 1

**b) x + 1 = 0**

**Ans:**Subtract i from both sides

x + 1 – 1 = 0 – 1

x = -1

**c) x – 1 = 5**

**Ans:**Add 1 to both sides

x – 1 + 1 = 5 + 1

x = 6

**d) x +6 = 2**

**Ans:**Subtract 6 from both sides

x + 6 – 6 = 2 – 6

x = -4

**e) y – 4 = -7**

**Ans:**Add 4 to both sides

y – 4 + 4 = -7 + 4

y = -3

**f) y – 4 = 0**

**Ans:**Add 4 to both sides

y – 4 + 4 = 0 + 4

y = 4

**g) y + 4 = 4**

**Ans:**Subtract 4 from both sides

y + 4 – 4 = 4 – 4

y = 0

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

**Ans:**Subtract 4 from both sides

y + 4 – 4 = – 4 – 4

y = -8

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

**Ans:**Divide both sides by 3

3l/3 = 42/3

l = 14

**b) b/(2 )= 6**

**Ans**: Multiply both sides by 2

b/2x 2 = 6 x 2

b = 12

**c) p/7 = 4**

**Ans:**Multiply both sides by 7

p/7x 7 = 4 x 7

P = 7

**d) 4x = 25**

**Ans:**Divide both sides by 4

4x/4 = 25/4

x = 25/4

**e) 8y = 36**

**Ans:**Divide both sides by

8y/8 = 36/8

y = 36/8

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

**Ans:**Multiply both sides by 3

z/3x 3 = 5/4 x 3

Z = 15/4

**g) a/15 = 7/15**

**Ans:**Multiply both sides by 5

a/5x 5 = 7/15 x 5

a = 7/3

**h) 20t = -10**

**Ans:**Divide both sides by 20

20t/20 = (-10)/20

t = (-1)/2

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

**Ans:**Step 1 – add 2 on both sides

3n – 2 + 2 = 46 + 2

3n = 48

Step2 – divide both sides by 3

3n/3 = 48/3

n = 16

**b) 5m + 7 = 17**

**Ans:**Step 1 – Subtract 7 on both sides

5m + 7 – 7 = 17 – 7

5m = 10

**c) 20p/3 = 40**

**Ans:**Step 1 – Multiply both sides by 3

20p/3x 3 = 40 x 3

Step 2 – Divide both sides by 20

20p/20 = 120/20

p = 6

**d) 3p/10 = 6**

**Ans:**Step 1 – Multiply both sides by 10

3p/( 10)x 10 = 6 x 10

3p = 60

Step 2 – Divide both sides by 3

3p/3 = 60/3

p = 20

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

**Ans:**Dividing both sides by 10

10p/10 = 100/10

p = 10

**b) 10p + 10 = 100**

**Ans:**Subtracting both sides by 10

10p + 10 – 10 = 100 – 10

10p = 90

Dividing both sides by 10

10p/10 = 90/10

p = 9

**c) p/4 = 5**

**Ans:**Multiplying both sides by 4

p/4x 4 = 5 x 4

p = 20

**d) p/3 = 5**

**Ans:**Multiplying both sides by 3

p/3x 3 = 5×3

p = 15

**e) 3p/4 = 6**

**Ans:**Multiplying both sides by 4

3p/4x 4 = 6 x 4

3p = 24

Dividing both sides by 3

3p/3 = 24/3

p = 8

**f) 3s = -9**

**Ans:**Dividing both sides by 3

3s/3 = (-9)/3

s = -3

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

**Ans:**Subtracting both sides by 12

3s + 12 – 12 = 0 – 12

3s = – 12

Dividing both sides by 3

3s/3 =(-12)/3

s = -4

**h) 3s = 0**

**Ans:**Dividing both sides by 3

3s/3 = 0/3

s = 0

**i) 2q = 6**

**Ans:**Dividing both sides by 2

2q/2 = 6/2

q = 3

**j) 2q – 6 = 0**

**Ans:**Adding 6 on both sides

2q – 6 + 6 = 0 + 6

2q = 6

Dividing both sides by 2

2q/2 = 6/2

q = 3

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

**Ans:**Subtracting both sides by 6

2q + 6 – 6 = 0 – 6

2q = -6

Dividing both sides by 2

2q/2 = (-6)/2

q = -3

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

**Ans:**Subtracting both sides by 6

2q + 6 – 6 = 12 – 6

2q = 6

Dividing both sides by 2

2q/2 = 6/2

q = 3