Exercise 4.2 Page: 86
1. Give first the step you will use to separate the variable and then solve the equation:
(a) x – 1 = 0
Solution:-
We have to add 1 to both the side of given equation,
Then we get,
= x – 1 + 1 = 0 + 1
= x = 1
(b) x + 1 = 0
Solution:-
We have to subtract 1 to both the side of given equation,
Then we get,
= x + 1 – 1 = 0 – 1
= x = – 1
(c) x – 1 = 5
Solution:-
We have to add 1 to both the side of given equation,
Then we get,
= x – 1 + 1 = 5 + 1
= x = 6
(d) x + 6 = 2
Solution:-
We have to subtract 6 to both the side of given equation,
Then we get,
= x + 6 – 6 = 2 – 6
= x = – 4
(e) y – 4 = – 7
Solution:-
We have to add 4 to both the side of given equation,
Then we get,
= y – 4 + 4 = – 7 + 4
= y = – 3
(f) y – 4 = 4
Solution:-
We have to add 4 to both the side of given equation,
Then we get,
= y – 4 + 4 = 4 + 4
= y = 8
(g) y + 4 = 4
Solution:-
We have to subtract 4 to both the side of given equation,
Then we get,
= y + 4 – 4 = 4 – 4
= y = 0
(h) y + 4 = – 4
Solution:-
We have to subtract 4 to both the side of given equation,
Then 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:-
Now we have to divide both sides of the equation by 3,
Then we get,
= 3l/3 = 42/3
= l = 14
(b) b/2 = 6
Solution:-
Now we have to multiply both sides of the equation by 2,
Then we get,
= b/2 × 2= 6 × 2
= b = 12
(c) p/7 = 4
Solution:-
Now we have to multiply both sides of the equation by 7,
Then we get,
= p/7 × 7= 4 × 7
= p = 28
(d) 4x = 25
Solution:-
Now we have to divide both sides of the equation by 4,
Then we get,
= 4x/4 = 25/4
= x = 25/4
(e) 8y = 36
Solution:-
Now we have to divide both sides of the equation by 8,
Then we get,
= 8y/8 = 36/8
= x = 9/2
(f) (z/3) = (5/4)
Solution:-
Now we have to multiply both sides of the equation by 3,
Then we get,
= (z/3) × 3 = (5/4) × 3
= x = 15/4
(g) (a/5) = (7/15)
Solution:-
Now we have to multiply both sides of the equation by 5,
Then we get,
= (a/5) × 5 = (7/15) × 5
= a = 7/3
(h) 20t = – 10
Solution:-
Now we have to divide both sides of the equation by 20,
Then 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:-
First we have to add 2 to the both sides of the equation,
Then, we get,
= 3n – 2 + 2 = 46 + 2
= 3n = 48
Now,
We have to divide both sides of the equation by 3,
Then, we get,
= 3n/3 = 48/3
= n = 16
(b) 5m + 7 = 17
Solution:-
First we have to subtract 7 to the both sides of the equation,
Then, we get,
= 5m + 7 – 7 = 17 – 7
= 5m = 10
Now,
We have to divide both sides of the equation by 5,
Then, we get,
= 5m/5 = 10/5
= m = 2
(c) 20p/3 = 40
Solution:-
First we have to multiply both sides of the equation by 3,
Then, we get,
= (20p/3) × 3 = 40 × 3
= 20p = 120
Now,
We have to divide both sides of the equation by 20,
Then, we get,
= 20p/20 = 120/20
= p = 6
(d) 3p/10 = 6
Solution:-
First we have to multiply both sides of the equation by 10,
Then, we get,
= (3p/10) × 10 = 6 × 10
= 3p = 60
Now,
We have to 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:-
Now,
We have to divide both sides of the equation by 10,
Then, we get,
= 10p/10 = 100/10
= p = 10
(b) 10p + 10 = 100
Solution:-
First we have to subtract 10 to the both sides of the equation,
Then, we get,
= 10p + 10 – 10 = 100 – 10
= 10p = 90
Now,
We have to divide both sides of the equation by 10,
Then, we get,
= 10p/10 = 90/10
= p = 9
(c) p/4 = 5
Solution:-
Now,
We have to multiply both sides of the equation by 4,
Then, we get,
= p/4 × 4 = 5 × 4
= p = 20
(d) – p/3 = 5
Solution:-
Now,
We have to multiply both sides of the equation by – 3,
Then, we get,
= – p/3 × (- 3) = 5 × (- 3)
= p = – 15
(e) 3p/4 = 6
Solution:-
First we have to multiply both sides of the equation by 4,
Then, we get,
= (3p/4) × (4) = 6 × 4
= 3p = 24
Now,
We have to divide both sides of the equation by 3,
Then, we get,
= 3p/3 = 24/3
= p = 8
(f) 3s = – 9
Solution:-
Now,
We have to divide both sides of the equation by 3,
Then, we get,
= 3s/3 = -9/3
= s = -3
(g) 3s + 12 = 0
Solution:-
First we have to subtract 12 to the both sides of the equation,
Then, we get,
= 3s + 12 – 12 = 0 – 12
= 3s = -12
Now,
We have to divide both sides of the equation by 3,
Then, we get,
= 3s/3 = -12/3
= s = – 4
(h) 3s = 0
Solution:-
Now,
We have to divide both sides of the equation by 3,
Then, we get,
= 3s/3 = 0/3
= s = 0
(i) 2q = 6
Solution:-
Now,
We have to divide both sides of the equation by 2,
Then, we get,
= 2q/2 = 6/2
= q = 3
(j) 2q – 6 = 0
Solution:-
First we have to add 6 to the both sides of the equation,
Then, we get,
= 2q – 6 + 6 = 0 + 6
= 2q = 6
Now,
We have to divide both sides of the equation by 2,
Then, we get,
= 2q/2 = 6/2
= q = 3
(k) 2q + 6 = 0
Solution:-
First we have to subtract 6 to the both sides of the equation,
Then, we get,
= 2q + 6 – 6 = 0 – 6
= 2q = – 6
Now,
We have to divide both sides of the equation by 2,
Then, we get,
= 2q/2 = – 6/2
= q = – 3
(l) 2q + 6 = 12
Solution:-
First we have to subtract 6 to the both sides of the equation,
Then, we get,
= 2q + 6 – 6 = 12 – 6
= 2q = 6
Now,
We have to divide both sides of the equation by 2,
Then, we get,
= 2q/2 = 6/2
= q = 3