NCERT Exercise 4.2 Solution-2
Simple Equations 7th Math
NCERT Exercise 4.2 Solution-2
Question (3) Give the steps you will use to separate the variable and then solve the equation:
Question (3)(a) 3n – 2 = 46
Solution
Given, 3n – 2 =46
After adding 2 to both sides, i.e. LHS and RHS, we get
3n – 2 + 2 = 46 + 2
⇒ 3n = 48
After dividing both sides by 3, we get
3n/3 = 48/3
⇒ n = 16
Thus, (i) adding 2 to both sides (ii) dividing both sides by 3, n = 16 Answer
Alternate method to solve an equation
Given, 3n – 2 = 46
After transposing –2 to RHS
[When a digit or variable is transposed to other side in an equation, its sign changed.]
Here, after transposing other side –2 is converted to +2
Thus, 3n = 46 + 2
⇒ 3n = 48
After transposing 3 to RHS
After transposing 3 to RHS it goes to denominator
Thus, n = 48/3
⇒ n = 16
Thus, (i) transposing of –2 to RHS (ii) Transposing of 3 to RHS, n = 16 Answer
Question (3)(b) 5 m + 7 = 17
Solution
Given, 5 m + 7 = 17
After subtracting 7 to both sides, i.e. to LHS and RHS, we get
5m + 7 – 7 = 17 – 7
⇒ 5m = 10
After dividing both sides by 5, we get
5 m/5 = 10/5
⇒ m = 2
Thus, (i) Subtracting 7 to both sides, (ii) Dividing both sides by 5, m = 2 Answer
Alternate method to solve an equation
Given, 5m + 7 = 17
After transposing 7 to RHS.
Here after transposing the +7 to RSH, it becomes –7
Thus, 5m = 17 – 7
⇒ 5m = 10
After transposing 5 to RHS
Here, after transposing to RHS 5 becomes 1/5
Thus, m = 10 × 1/5
Thus, m = 2
Thus, (i) transposing of 7 to RHS (ii) transposing of 5 to RHS, m = 2 Answer
Question (3)(c) 20 p/3 = 40
Solution
Given, 20 p/3 = 40
After multiplying both sides with 3, we get
20 p/3 × 3 = 40 × 3
⇒ 20 p = 120
After dividing both sides by 20, we get
20 p/20 = 120/20
⇒ p = 6
Thus, (i) multiplying both sides with 3 (ii) dividing both side by 20, p = 6 Answer
Alternate method to solve an equation
Given, 20 p/3 = 40
After transposing 3 to RHS
After transposing 3 is multiplied in RHS
Thus, 20 p = 40 × 3
⇒ 20 p = 120
After transposing 20 to RHS
After transposing, 20 will goes to denominator in RHS
Thus, p = 120/20
⇒ p = 6
Thus, (i) transposing of 3 to RHS (ii) Transposing of 20 to RHS, p = 6 Answer
Question (3)(d) 3 p/10 = 6
Solution
Given, 3 p/10 = 6
After multiplying both sides by 10, we get
3 p/10 × 10 = 6 × 10
⇒ 3 p = 60
After dividing both sides by 3, we get
3p/3 = 60/3
⇒ p = 20
Thus, (i) multiplying both sides by 10 (ii) dividing both sides by 3, p = 20 Answer
Alternate method to solve an equation
Given, 3 p/10 = 6
After transposing 10 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 10 is in LHS in denominator, thus, it will become in multiplication in RHS
Thus, 3 p = 6 × 10
⇒ 3 p = 60
After transposing 3 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 3 will become in division, i.e. goes to denominator after transposing to RHS
Thus, p = 60/3
⇒ p = 20
Thus, (i) transposing of 10 to RHS (ii) transposing of 3 to RHS, p = 20 Answer
Question (4) Solve the following equations:
Question (4)(a) 10 p = 100
Solution
Given, 10 p = 100
After dividing both sides by 10, we get
10 p/10 = 100/10
⇒ p = 10
Thus, p = 10 Answer
Alternate method to solve an equation
Given, 10 p =100
After transposing 10 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 10 will become in division, i.e. goes to denominator after transposing to RHS
Thus, p = 100/10
⇒ p = 10
Thus, p = 10 Answer
Question (4)(b) 10 p + 10 = 100
Solution
Given, 10 p + 10 = 100
After subtracting 10 to both sides, we get
10 p + 10 – 10 = 100 – 10
⇒ 10 p = 90
After dividing both sides by 10, we get
10 p/10 = 90/10
⇒ p = 9
Thus, p = 9 Answer
Alternate method to solve an equation
Given, 10 p + 10 = 100
After transposing 10 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +10 will become –10 when transposed to RHS
Thus, 10 p = 100 – 10
⇒ 10 p = 90
After transposing 10 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 10 will become in division, i.e. goes to denominator after transposing to RHS
Thus, p =90/10
⇒ p = 9
Thus, p = 9 Answer
Question (4)(c) p/4 = 5
Solution
Given, p/4 = 5
After multiplying both sides by 4, we get
p/4 × 4 = 5 × 4
⇒ p = 20
Thus, p = 20 Answer
Alternate method to solve an equation
Given, p/4 = 5
After transposing 4 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 4 is in LHS in denominator, thus, it will become in multiplication in RHS
Thus, p = 5 × 4
Thus, p = 20 Answer
Question (4)(d)– p/3 = 5
Solution
Given, – p/3 = 5
After multiplying both sides by 3, we get
– p/3 × 3 = 5 × 3
⇒ – p = 15
⇒ p = – 15
Thus, p = – 15 Answer
Alternate method to solve an equation
Given, – p/3 = 5
After transposing 3 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 3 in LHS is in denominator, thus, it will become in multiplication in RHS
Thus, – p = 5 × 3
⇒ –p = 15
⇒ p = –15
Thus, p = –15 Answer
Question (4)(e) 3 p/4 = 6
Solution
Given, 3 p/4 = 6
After multiplying both sides by 4, we get
3 p/4 × 4 = 6 × 4
⇒ 3 p = 24
After dividing both sides by 3, we get
3 p/3 = 24/3
⇒ p = 8
Thus, p = 8 Answer
Alternate method to solve an equation
Given, 3 p/4 = 6
After transposing 4 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 4 in LHS is in denominator, thus, it will become in multiplication in RHS
Thus, 3p = 6 × 4
⇒ 3 p = 24
After transposing 3 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 3 will become in division, i.e. goes to denominator after transposing to RHS
Thus, p = 24/3
⇒ p = 8
Thus, p = 8 Answer
(f) 3s = –9
Solution
Given, 3 s = –9
After dividing both sides by 3, we get
3s/3 = – 9/3
⇒ s = – 3
Thus, s = – 3 Answer
Alternate method to solve an equation
Given, 3 s = –9
After transposing 3 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 3 will become in division, i.e. goes to denominator after transposing to RHS
Thus, s = – 9/3
⇒ s = –3
Thus, s = –3 Answer
Question (4)(g) 3s + 12 = 0
Solution
Given, 3s + 12 = 0
After subtracting 12 to both sides, we get
3s + 12 – 12 = 0 – 12
⇒ 3s = –12
After dividing both sides by 3, we get
3s/3 = – 12/3
⇒ s = –4
Thus, s = –4 Answer
Alternate method to solve an equation
Given, 3s + 12 = 0
After transposing 12 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +12 will become –12 when transposed to RHS
Thus, 3s = 0 – 12
⇒ 3s = – 12
After transposing 3 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 3 will become in division, i.e. goes to denominator after transposing to RHS
Thus, s = – 12/3
⇒ s = – 4
Thus, s = –4 Answer
Question (4)(h) 3s = 0
Solution
Given, 3s = 0
After dividing both sides by 3, we get
3s/3 = 0/3
⇒ s = 0
Thus, s = 0 Answer
Alternate method to solve an equation
Given, 3s = 0
After transposing 3 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 3 will become in division, i.e. goes to denominator after transposing to RHS
Thus, s = 0/3
⇒ s = 0
Thus, s = 0 Answer
(i) 2q = 6
Solution
Given, 2q = 6
After dividing both sides by 2, we get
2q/2 = 6/2
⇒ q = 3
Thus, q = 3 Answer
Alternate method to solve an equation
Given, 2q = 6
After transposing 2 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 2 will become in division, i.e. goes to denominator after transposing to RHS
Thus, q = 6/2
⇒ q = 3
Thus, q = 3 Answer
Question (4)(j) 2q – 6 = 0
Solution
Given, 2q – 6 = 0
After adding 6 to both sides, we get
2q – 6 + 6 = 0 + 6
⇒ 2q = 6
After dividing both sides by 2, we get
2 q/2 = 6/2
⇒ q = 3
Thus, q = 3 Answer
Alternate method to solve an equation
Given, 2q – 6 = 0
After transposing –6 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, –6 will become +6 when transposed to RHS
⇒ 2q = 0 + 6
⇒ 2q = 6
After transposing 2 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 2 will become in division, i.e. goes to denominator after transposing to RHS
Thus, q = 6/2
⇒ q = 3
Thus, q = 3 Answer
(k) 2q + 6 = 0
Solution
Given, 2q + 6 = 0
After subtracting 6 to both sides, we get
2q + 6 – 6 = 0 – 6
⇒ 2q = –6
After dividing both sides by 2, we get
2q/2 = – 6/2
⇒ q = –3
Thus, q = –3 Answer
Alternate method to solve an equation
Given, 2q + 6 = 0
After transposing +6 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, 6 will become – 6 when transposed to RHS
⇒ 2q = 0 – 6
⇒ 2q = – 6
After transposing 2 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 2 will become in division, i.e. goes to denominator after transposing to RHS
Thus, q = – 6/2
⇒ q = – 3
Thus, q = – 3 Answer
Question (4)(ℓ) 2q + 6 = 12
Solution
Given, 2q + 6 = 12
After subtracting 6 to both sides, we get
2q + 6 – 6 = 12 – 6
⇒ 2q = 6
After dividing both sides by 2, we get
2 q/2 = 6/2
⇒ q = 3
Thus, q = 3 Answer
Alternate method to solve an equation
Given, 2q + 6 = 12
After transposing 6 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +6 will become –6 when transposed to RHS
⇒ 2q = 12 – 6
⇒ 2q = 6
After transposing 2 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 2 will become in division, i.e. goes to denominator after transposing to RHS
⇒ q = 6/2
⇒ q = 3
Thus, q = 3 Answer
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