1. Give first the step you will use to separate the variable and then solve the equation:
(a) x – 1 = 0
Solution:
Adding 1 to both the side of given equation,
we get,
x – 1 + 1 = 0 + 1
x = 1
(b) x + 1 = 0
Solution:
Subtracting 1 to both the side of given equation,
we get,
x + 1 – 1 = 0 – 1
x = – 1
(c) x – 1 = 5
Solution:
Adding 1 to both the side of given equation,
we get,
x – 1 + 1 = 5 + 1
x = 6
(d) x + 6 = 2
Solution:
Substracting 6 to both the side of given equation,
we get,
x + 6 – 6 = 2 – 6
x = – 4
(e) y – 4 = – 7
Solution:
Adding 4 to both the side of given equation,
we get,
y – 4 + 4 = – 7 + 4
y = – 3
(f) y – 4 = 4
Solution:
Adding 4 to both the side of given equation,
we get,
y – 4 + 4 = 4 + 4
y = 8
(g) y + 4 = 4
Solution:
Substracting 4 to both the side of given equation,
we get,
= y + 4 – 4 = 4 – 4
= y = 0
(h) y + 4 = – 4
Solution:
Substracting 4 to both the side of given equation,
we get,
= 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
Solution:
Dividing both sides of the equation by 3,
we get,
3l/3 = 42/3
l = 14
(b) b/2 = 6
Solution:
Multiplying both sides of the equation by 2,
we get,
b/2 × 2= 6 × 2
b = 12
(c) p/7 = 4
Solution:
Multiplying both sides of the equation by 7,
we get,
p/7 × 7= 4 × 7
p = 28
(d) 4x = 25
Solution:
Dividing both sides of the equation by 4,
we get,
4x/4 = 25/4
x = 25/4
(e) 8y = 36
Solution:
Dividing both sides of the equation by 8,
we get,
8y/8 = 36/8
x = 9/2
(f) (z/3) = (5/4)
Solution:
Multiplying both sides of the equation by 3,
we get,
(z/3) × 3 = (5/4) × 3
x = 15/4
(g) (a/5) = (7/15)
Solution:
Multiplying both sides of the equation by 5,
we get,
(a/5) × 5 = (7/15) × 5
a = 7/3
(h) 20t = – 10
Solution:
Dividing both sides of the equation by 20,
we get,
20t/20 = -10/20
x = – ½
3. Give the steps you will use to separate the variable and then solve the equation:
(a) 3n – 2 = 46
Solution:
In step 1 we add 2 to the both sides of the equation,
we get,
3n – 2 + 2 = 46 + 2
= 3n = 48
In step 2 we divide both sides of the equation by 3,
we get,
3n/3 = 48/3
n = 16
(b) 5m + 7 = 17
Solution:
In step 1 we subtract 7 to the both sides of the equation,
we get,
5m + 7 – 7 = 17 – 7
5m = 10
In step 2 we divide both sides of the equation by 5,
we get,
5m/5 = 10/5
m = 2
(c) 20p/3 = 40
Solution:
In step 1 we multiply both sides of the equation by 3,
we get,
(20p/3) × 3 = 40 × 3
20p = 120
In step 2 we divide both sides of the equation by 20,
we get,
20p/20 = 120/20
p = 6
(d) 3p/10 = 6
Solution:
In step 1 we multiply both sides of the equation by 10,
we get,
(3p/10) × 10 = 6 × 10
3p = 60
In step 2 we divide both sides of the equation by 3,
Then, we get,
3p/3 = 60/3
p = 20
4. Solve the following equations:
(a) 10p = 100
Solution:
Dividing both sides of the equation by 10,
we get,
10p/10 = 100/10
p = 10
(b) 10p + 10 = 100
Solution:
Subtracting 10 to the both sides of the equation,
we get,
10p + 10 – 10 = 100 – 10
10p = 90
Now,
Dividing both sides of the equation by 10,
we get,
10p/10 = 90/10
p = 9
(c) p/4 = 5
Solution:
Multiplying both sides of the equation by 4,
we get,
p/4 × 4 = 5 × 4
p = 20
(d) – p/3 = 5
Solution:
Multiplying both sides of the equation by – 3,
we get,
– p/3 × (- 3) = 5 × (- 3)
p = – 15
(e) 3p/4 = 6
Solution:
Multiplying both sides of the equation by 4,
we get,
(3p/4) × (4) = 6 × 4
3p = 24
Now,
Dividing both sides of the equation by 3,
we get,
3p/3 = 24/3
p = 8
(f) 3s = – 9
Solution:
Dividing both sides of the equation by 3,
we get,
3s/3 = -9/3
s = -3
(g) 3s + 12 = 0
Solution:
Substracting 12 to the both sides of the equation,
we get,
3s + 12 – 12 = 0 – 12
3s = -12
Now,
Dividing both sides of the equation by 3,
we get,
3s/3 = -12/3
s = – 4
(h) 3s = 0
Solution:
Dividing both sides of the equation by 3,
we get,
3s/3 = 0/3
s = 0
(i) 2q = 6
Solution:
Dividing both sides of the equation by 2,
we get,
2q/2 = 6/2
q = 3
(j) 2q – 6 = 0
Solution:
Adding 6 to the both sides of the equation,
we get,
2q – 6 + 6 = 0 + 6
2q = 6
Now,
Dividing both sides of the equation by 2,
we get,
2q/2 = 6/2
q = 3
(k) 2q + 6 = 0
Solution:
Subtracting 6 to the both sides of the equation,
we get,
2q + 6 – 6 = 0 – 6
2q = – 6
Now,
Dividing both sides of the equation by 2,
we get,
2q/2 = – 6/2
q = – 3
(l) 2q + 6 = 12
Solution:
Subtracting 6 to the both sides of the equation,
we get,
2q + 6 – 6 = 12 – 6
2q = 6
Now,
Dividing both sides of the equation by 2,
we get,
2q/2 = 6/2
q = 3
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