NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Exercise 4.2

NCERT Solutions for Class 7 Maths
Chapter 4 Simple Equations
Exercise 4.2

1. 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

Answer

☛ In such questions, to separate the given variable, we eliminate the numbers, which are given with variable. We can eliminate those numbers by multi-operations like add, subtract, multiplication etc.

(a) We have, x-1 =0

On adding 1 to both sides, we get

x-1+1 = 0+1 ⇒ x=1

Hence, x=l is the solution of the given equation.

(b) We have, x+1 =0

On subtracting 1 from both sides, we get
x+1-1 ⇒ 0 -1 ⇒ x= -1

Hence, x = – 1 is the solution of the given equation.

On adding 1 to both sides, we get

x-1+1 =5+1 ⇒ x=6

Hence, x=6 is the solution of the given equation.

(d) We have, x +6 =2

On subtracting 6 from both sides, we get x+6-6 = 2-6 ⇒ x=-4

Hence, x=-4 is the solution of the given equation.

(e) We have, y-4 =-7

On adding 4 to both sides, we get

y-4+4 =-7+4 ⇒ y=-3

Hence, y =-3 is the solution of the given equation.

(f) We have, y – 4=4

On adding 4 to both sides, we get

y-4+4 =4+4 ⇒ y=8

Hence, y = 8 is the solution of the given equation.

(g) We have, y+ 4 =4

On subtracting 4 from both sides, we get

y+4-4 = 4-4 ⇒ y=8

Hence, y=0 is the solution of the given equation.

(h) We have, y + 4 = -4

On subtracting 4 from both sides, we get

y+4-4 = -4-4 ⇒ y=-8

Hence, y=-8 is the solution of the given equation.

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

Answer

(a) 3l = 42
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
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
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
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
Now we have to divide both sides of the equation by 8,
Then we get,
= 8y/8 = 36/8
= y = 9/2

(f) (z/3) = (5/4)
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)
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
Now we have to divide both sides of the equation by 20,
Then we get,
= 20t/20 = -10/20
= t = – ½

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

Answer

(a) 3n – 2 = 46
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
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
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
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 (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

Answer

(a) 10p = 100
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
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
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
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
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
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
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
Now, we have to divide both sides of the equation by 3,
Then, we get,
= 3s/3 = 0/3
= s = 0

(i) 2q = 6
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
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
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
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

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