NCERT Solutions Class 7 Mathematics Simple Equations Ex 4.2

Question : 1.Give first the step you will use to separate the variable and then solve the equations:
(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 :
(a) x – 1 = 0

⇒ x – 1 + 1 = 0 + 1 [Adding 1 both sides]

⇒ x = 1

(b) x + 1 = 0

⇒ x + 1 – 1 = 0 – 1 [Subtracting 1 both sides]

⇒ x = –1

(c) x – 1 = 5

⇒ x – 1 + 1 = 5 + 1 [Adding 1 both sides]

⇒ x = 6

(d) x + 6 = 2

⇒ x + 6 – 6 = 2 – 6 [Subtracting 6 both sides]

⇒ x = –4

(e) y – 4 = –7

⇒ y – 4 + 4 = –7 + 4 [Adding 4 both sides]

⇒ y = –3

(f) y – 4 = 4

⇒ y – 4 + 4 = 4 + 4 [Adding 4 both sides]

⇒ y = 8

(g) y + 4 = 4

⇒ y + 4 – 4 = 4 – 4 [Subtracting 4 both sides]

⇒ y = 0

(h) y + 4 = –4

⇒ y + 4 – 4 = –4 –4 [Subtracting 4 both sides]

⇒ y = –8

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

⇒ 3l 3 = 423 [Dividing both sides by 3]

⇒ l = 14

(b) ^b⁄₂ = 6

⇒ ^b⁄₂ × 2 = 6 × 2 [Multiplying both sides by 2]

⇒ b = 12

(c) ^p⁄₇ = 4

⇒ ^p⁄₇ × 7 = 4 × 7 [Multiplying both sides by 7]

⇒ p = 28

(d) 4x = 25

⇒ ^4x⁄₄ = ²⁵⁄₄ [Dividing both sides by 4]

⇒ x = ²⁵⁄₄

(e) 8y = 36

⇒ ^8y⁄₈ = ³⁶⁄₈ [Dividing both sides by 8]

⇒ y = ⁹⁄₂

(f) ^z⁄₃ = ⁵⁄₄

⇒ ^z⁄₃ × 3 = ⁵⁄₄ × 3 [Multiplying both sides by 3]

⇒ z = ¹⁵⁄₄

(g) ^a⁄₅ = ⁷⁄₁₅

⇒ ^a⁄₅ x 5 = ^a⁄₁₅ x 5 [Multiplying both sides by 5]

⇒ a = ⁷⁄₃

(h) 20t = –10

⇒ ^20t⁄₂₀ = ^{– 10}⁄₂₀ [Dividing both sides by 20]

⇒ t = ^{– 1}⁄₂

Question : 3 Give first the step you will use to separate the variable and then solve the equations
(a) 3n – 2 = 46

(b) 5m + 7 = 17

(c) ^20p⁄₃ = 40

(d) ^3p⁄₁₀ = 6

Answer :
(a) 3n – 2 = 46

Step I: 3n – 2 +2 = 46 + 2

⇒ 3n = 48

[Adding 2 both sides]

Step II: ³ⁿ⁄₃ = ⁴⁸⁄₃

⇒ n = 16 [Dividing both sides by 3]

(b) 5m + 7 = 17

Step I: 5m + 7 – 7 = 17 – 7 ⇒ 5m = 10 [Subtracting 7 both sides]

Step II: ^a⁄₅ = ¹⁰⁄₅

⇒ m = 2 [Dividing both sides by 5]

(c) ^20p⁄₃ = 40

Step I: ^20p⁄₃ × 3 = 40 × 3 ⇒ 20p = 120 [Multiplying both sides by 3]

Step II: ^20p⁄₂₀ = ¹²⁰⁄₂₀

⇒ p = 6 [Dividing both sides by 20]

(d) ^3p⁄₁₀ = 6

Step I: ^3p⁄₁₀ × 10 = 6 × 10

⇒ 3p = 60 [Multiplying both sides by 10]

Step II: ^3p⁄₃ = ⁶⁰⁄₃ ⇒ p = 20 [Dividing both sides by 3]

Question : 4.Solve the following equation:
(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

⇒ ^10p⁄₁₀ = ¹⁰⁰⁄₁₀ [Dividing both sides by 10]

⇒ p = 10

(b) 10p + 10 = 100

⇒ 10p + 10 – 10 = 100 – 10 [Subtracting both sides 10]

⇒ 10p = 90

⇒ ^10p⁄₁₀ = ⁹⁰⁄₁₀ [Dividing both sides by 10]

⇒ p = 9

(c) ^p⁄₄ = 5

⇒ ^p⁄₄ × 4 = 5 × 4 [Multiplying both sides by 4]

⇒ p = 20

(d) ^-p⁄₃ = 5

⇒ ^-p⁄₃ × (–3) = 5 × (–3) [Multiplying both sides by – 3]

⇒ p = –15

(e) ^3p⁄₄ = 6

⇒ ^3p⁄₄ × 4 = 6 × 4 [Multiplying both sides by 4]

⇒ 3p = 24

⇒ ^3p⁄₃ = ²⁴⁄₃ [Dividing both sides by 3]

⇒ p = 8