Simple Equations
Exercise 4.2
1). Give first the step you will use to separate the variable and then solve the equation:
(a) x – 1 = 0 (b) x + 1 = 0
(c) x – 1 = 5 (d) x + 6 = 2
(e) y – 4 = – 7 (f) y – 4 = 4
(g) y + 4 = 4 (h) y + 4 = – 4
Solution:
(a) x – 1 = 0
Adding 1 to both the sides
x – 1 + 1 = 0 + 1
x – 0 = 1
x = 1
(b) x + 1 = 0
subtracting 1 to both the sides
x + 1 – 1 = 0 – 1
x + 0 = -1
x = -1
(c) x – 1 = 5
Adding 1 to both the sides
x – 1 + 1 = 5 + 1
x – 0 = 6
x = 6
(d) x + 6 = 2
subtracting 6 from both the sides
x + 6 – 6 = 2 – 6
x + 0 = -4
x = -4
(e) y – 4 = – 7
Adding 4 to both the sides
y – 4 + 4 = -7 + 4
y – 0 = -3
y = -3
(f) y – 4 = 4
Adding 4 to both the sides
y – 4 + 4 = 4 + 4
y – 0 = 8
y = 8
(g) y + 4 = 4
subtracting 4 from both the sides
y + 4 – 4 = 4 – 4
y + 0 = 0
y = 0
(h) y + 4 = – 4
subtracting 4 from both the sides
y + 4 – 4 = -4 – 4
y + 0 = -8
y = -8
2). Give first the step you will use to separate the variable and then solve the equation:
(a) 3l = 42 (b)b/2 = 6
(c) p/7 = 4 (d) 4x = 25
(e) 8y = 36 (f) z/3 = 5/4
(g) a/5 = 7/15 (h) 20t = – 10
Solution:
(a) 3l = 42 (b)b/2 = 6
(c) p/7 = 4 (d) 4x = 25
(e) 8y = 36 (f) z/3 = 5/4
(g) a/5 = 7/15 (h) 20t = – 10
3). Give the steps you will use to separate the variable and then solve the equation:
(a) 3n – 2 = 46 (b) 5m + 7 = 17
(c) 20p/3 = 40 (d) 3p / 10 = 6
Solution
(a) 3n – 2 = 46
Adding 2 to both the sides
3n – 2 + 2 = 46 + 2
3n = 48
Dividing both the sides by 3
3n /3 = 48/3
n = 16
(b) 5m + 7 = 17
Subtracting 7 from both the sides
5m + 7 – 7 = 17 – 7
5m = 10
Dividing both the sides by 5
5m /5 = 10/5
m = 2
(c) 20p/3 = 40
Multiplying 3 to both the sides
20p/3 X 3 = 40 X 3
20p = 120
Dividing both the sides by 20
20p /20 = 120/20
p = 6
(d) 3p / 10 = 6
Multiplying 10 to both the sides
3p/10 X 10 = 6 X 10
3p = 60
Dividing both the sides by 20
3p /3 = 60/3
p = 20
4). Solve the following equations:
(a) 10p = 100 (b) 10p + 10 = 100
(c) p/4 = 5 (d) –p /3 = 5
(e) 3p / 4 = 6 (f) 3s = –9
(g) 3s + 12 = 0 (h) 3s = 0
(i) 2q = 6 (j) 2q – 6 = 0
(k) 2q + 6 = 0 (l) 2q + 6 = 12
Solution
(a) 10p = 100
Dividing both the sides by 10
10p/10 = 100/10
p = 10
(b) 10p + 10 = 100
Subtracting 10 from both the sides
10p + 10 – 10 = 100 – 10
10p = 90
Dividing both the sides by 10
10p/10 = 90/10
p = 9
(c) p/4 = 5
Multiplying both the sides by 4
p/4 X 4 = 5 X 4
p = 20
(d) –p /3 = 5
Multiplying both the sides by 3
–p /3 X 3 = 5 X 3
–p = 15
p = -15
(e) 3p / 4 = 6
Multiplying both the sides by 4
3p /4 X 4 = 6 X 4
3p = 24
Dividing both the sides by 3
3p/3 = 24/3
3p = 8
(f) 3s = –9
Dividing both the sides by 3
3s / 3 = -9/3
s = -3
(g) 3s + 12 = 0
Subtracting 12 from both the sides
3s + 12 – 12 = 0 – 12
3s = -12
Dividing both the sides by 3
3s/3 = -12/3
s = -4
(h) 3s = 0
Dividing both the sides by 3
3s/3 = 0/3
s = 0
(i) 2q = 6
Dividing both the sides by 2
2q/2 = 6/2
q = 3
(j) 2q – 6 = 0
Adding both the sides by 6
2q – 6 + 6 = 0 + 6
2q = 6
q = 3
(k) 2q + 6 = 0
Subtracting 6 from both the sides
2q + 6 – 6 = 0 – 6
2q = -6
Dividing both the sides by 2
2q/2 = -6/2
q = -3
(l) 2q + 6 = 12
Subtracting 6 from both the sides
2q + 6 – 6 = 12 – 6
2q = 6
Dividing both the sides by 2
2q/2 = 6/2
q = 3
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