Exercise 4.3 - Chapter 4 Simple Equations class 7 ncert solutions Maths - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question 1:

Solve the following equations.

(a)   (b) 5t + 28 = 10 (c) 

(d)   (e)   (f) 

(g)   (h) 6z + 10 = − 2 (i) 

(j) 

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,

(g) 

 (Transposing   to R.H.S.)

Dividing both sides by 7,

(h) 6z + 10 = −2

6z = − 2 − 10 = −12 (Transposing 10 to R.H.S.)

Dividing both sides by 6,

(i) 

Multiplying both sides by 2,

Dividing both sides by 3,

(j) 

 (Transposing −5 to R.H.S.)

Multiplying both sides by 3,

2b = 8 × 3 = 24

Dividing both sides by 2,

b =  = 12

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)