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