Class-7 Maths Chapter-4 Exercise 4.2 Simple equations

EVENTS CONVENT HIGH SCHOOL

12/01/2021                       CLASS-7                                  SLOT-2

MATHS

Chapter-4 SIMPLE EQUATIONS

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Exercise-4.2 

Question 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

 

Answer:(a) x − 1 = 0

Adding 1 to both sides of the given equation, we obtain

x − 1 + 1 = 0 + 1

x = 1

(b) x + 1 = 0

Subtracting 1 from both sides of the given equation, we obtain

x + 1 − 1 = 0 − 1

x = −1

(c) x − 1 = 5

Adding 1 to both sides of the given equation, we obtain

x − 1 + 1 = 5 + 1

x = 6

(d) x + 6 = 2

Subtracting 6 from both sides of the given equation, we obtain

x + 6 − 6 = 2 − 6

x = −4

(e) y − 4 = −7

Adding 4 to both sides of the given equation, we obtain

y − 4 + 4 = − 7 + 4

y = −3

(f) y − 4 = 4

Adding 4 to both sides of the given equation, we obtain

y − 4 + 4 = 4 + 4

y = 8

Question 2:Give first the step you will use to separate the variable and then solve the equation:

(a) 3l = 42 (b)  (c) 

(d) 4x = 25 (e) 8y = 36 (f) 

(g)  (h) 20t = − 10

Answer:

(a) 3l = 42

Dividing both sides of the given equation by 3, we obtain

l = 14

(b) 

Multiplying both sides of the given equation by 2, we obtain

b = 12

(c) 

Multiplying both sides of the given equation by 7, we obtain

p = 28

(d) 4x = 25

Dividing both sides of the given equation by 4, we obtain

x = 

(e) 8y = 36

Dividing both sides of the given equation by 8, we obtain

y = 

(f) 

Multiplying both sides of the given equation by 3, we obtain

(g) 

Multiplying both sides of the given equation by 5, we obtain 

(h) 20t = −10

Dividing both sides of the given equation by 20, we obtain

Question 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) 

(d) 

Answer:

(a) 3n − 2 = 46

Adding 2 to both sides of the given equation, we obtain

3n − 2 + 2 = 46 + 2

3n = 48

Dividing both sides of the given equation by 3, we obtain

n = 16

(b) 5m + 7 = 17

Subtracting 7 from both sides of the given equation, we obtain

5m + 7 − 7 = 17 − 7

5m = 10

Dividing both sides of the given equation by 5, we obtain

(c) 

Multiplying both sides of the given equation by 3, we obtain

Dividing both sides of the given equation by 20, we obtain

(d)

Multiplying both sides of the given equation by 10, we obtain

Dividing both sides of the given equation by 3, we obtain

p = 20

Question 4:Solve the following equations:

(a) 10p = 100 (b) 10p + 10 = 100 (c) 

(d)  (e)  (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) 10 p = 100

(b) 10 p + 10 = 100

10 p + 10 − 10 = 100 − 10

10 p = 90

(c) 

(d) 

(e)

(f) 3 s = −9

(g) 3 s + 12 = 0

3 s + 12 − 12= 0 − 12

3 s = −12

(h) 3 s = 0

(i) 2q = 6

(j) 2q − 6 = 0

2q − 6 + 6 = 0 + 6

2q = 6

(k) 2q + 6 = 0

2q + 6 − 6 = 0 − 6

2q = −6

(l) 2q + 6 = 12

2q + 6 − 6 = 12 − 6

2q = 6

Exercise-4.3

Question 1:Solve the following equations.

(a)  (b) 5t + 28 = 10 (c) 

(d)  (e)  (f) 

Answer:

(a) 

 (Transposing to R.H.S.)

Dividing both sides by 2,

(b) 5t + 28 = 10

5t = 10 − 28 = −18 (Transposing 28 to R.H.S.)

Dividing both sides by 5,

(c) 

 (Transposing 3 to R.H.S.)

Multiplying both sides by 5,

a = −1 × 5 = −5

(d) 

 (Transposing 7 to R.H.S.)

Multiplying both sides by 4,

q = −8

(e) 

Multiplying both sides by 2,

5x = −10 × 2 = −20

Dividing both sides by 5,

(f) 

Multiplying both sides by 2,

Dividing both sides by 5,

Question 2:Solve the following equations.

(a) 2 (x + 4) = 12 (b) 3 (n − 5) = 21

(c) 3 (n − 5) = − 21 (d) −4 (2 + x) = 8

(e) 4(2 − x) = 8

Answer:

(a) 2 (x + 4) = 12

Dividing both sides by 2,

x = 6 − 4 = 2 (Transposing 4 to R.H.S.)

(b) 3 (n − 5) = 21

Dividing both sides by 3,

n = 7 + 5 = 12 (Transposing −5 to R.H.S.)

(c) 3 (n − 5) = −21

Dividing both sides by 3,

n = − 7 + 5 = −2 (Transposing −5 to R.H.S.)

(d) −4 (2 + x) = 8

Dividing both sides by −4,

x = − 2 − 2 = −4 (Transposing 2 to R.H.S.)

(e) 4 (2 − x) = 8

Dividing both sides by 4,

2 − x = 2

−x = 2 − 2 (Transposing 2 to R.H.S.)

−x = 0

x = 0

Question 3:

Solve the following equations.

(a) 4 = 5 (p − 2)         (b) − 4 = 5 (p − 2)

(c) 16 = 4 + 3 (t + 2)   (d) 4 + 5 (p − 1) = 34

(e) 0 = 16 + 4 (m − 6)

Answer:

(a) 4 = 5 (p − 2)

Dividing both sides by 5,

(b) − 4 = 5 (p − 2)

Dividing both sides by 5,

(c) 16 = 4 + 3 (t + 2)

16 − 4 = 3 (t + 2) (Transposing 4 to L.H.S.)

12 = 3 (t + 2)

Dividing both sides by 3,

4 = t + 2

4 − 2 = t (Transposing 2 to L.H.S.)

2 = t

(d) 4 + 5 (p − 1) = 34

5 (p − 1) = 34 − 4 = 30 (Transposing 4 to R.H.S.)

Dividing both sides by 5,

p = 6 + 1 = 7 (Transposing −1 to R.H.S.)

(e) 0 = 16 + 4 (m − 6)

0 = 16 + 4m − 24

0 = −8 + 4m

4m = 8 (Transposing −8 to L.H.S)

Dividing both sides by 4,

m = 2

Question 4:

(a) Construct 3 equations starting with x = 2

(b) Construct 3 equations starting with x = − 2

Answer:

(a) x = 2

Multiplying both sides by 5,

5x = 10 (i)

Subtracting 3 from both sides,

5x − 3 = 10 − 3

5 x − 3 = 7 (ii)

Dividing both sides by 2,

(b) x = −2

Subtracting 2 from both sides,

x − 2 = − 2 − 2

x − 2 = −4 (i)

Again, x = −2

Multiplying by 6,

6 × x = −2 × 6

6x = −12

Subtracting 12 from both sides,

6x − 12 = − 12 − 12

6x − 12 = −24 (ii)

Adding 24 to both sides,

6x − 12 + 24 = − 24 + 24

6x + 12 = 0 (iii)

EXERCISE 4.4

Question 1:Set up equations and solve them to find the unknown numbers in the following cases:

(a) Add 4 to eight times a number; you get 60.

(b) One-fifth of a number minus 4 gives 3.

(c) If I take three-fourths of a number and add 3 to it, I get 21.

(d) When I subtracted 11 from twice a number, the result was 15.

Answer:(a) Let the number be x.

8 times of this number = 8x

8x + 4 = 60

8x = 60 − 4 (Transposing 4 to R.H.S.)

8x = 56

Dividing both sides by 8,

(b) Let the number be x.

One-fifth of this number = 

 (Transposing −4 to R.H.S.)

Multiplying both sides by 5,

(c) Let the number be x.

Three-fourth of this number = 

 (Transposing 3 to R.H.S.)

Multiplying both sides by 4, 

Dividing both sides by 3,

(d) Let the number be x.

Twice of this number = 2x

2x − 11 = 15

2x = 15 + 11 (Transposing −11 to R.H.S.)

2x = 26

Dividing both sides by 2,

x = 13