NCERT Exercise 4.3 Solution
Simple Equations 7th Math
NCERT Exercise 4.3 Solution
Question (1) Solve the following equations
Question (1) (a) 2y + 5/2 = 37/2
Solution
Given, 2y + 5/2 = 37/2
After subtracting 5/2 from both sides, we get
2y + 5/2 – 5/2 = 37/2 – 5/2
⇒ 2 y = 37 – 5/2
⇒ 2 y = 32/2
⇒ 2y = 16
After dividing both sides by 2, we get
2y/2 = 16/2
⇒ y = 8
Thus, y = 8 Answer
Alternate Method to solve an equation
Given, 2y + 5/2 = 37/2
After transposing 5/2 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, 5/2 will become – 5/2 when transposed to RHS
Thus, 2y = 37/2 – 5/2
⇒ 2y = 37 – 5/2
⇒ 2y = 32/2
⇒ 2y = 16
After transposing 2 to RHS, we get
When a number or digit which is in multiple in one side is transposed to other side, it goes in denominator.
Thus, here 2 becomes 1/2 after transposing to RHS
Thus, y = 16/2
⇒ y = 8
Thus, y = 8 Answer
Question (1)(b) 5t + 28 = 10
Solution
Given, 5t + 28 = 10
After subtracting 28 from both sides, we get
5t + 28 – 28 = 10 – 28
⇒ 5t = – 18
After dividing both sides by 5, we get
5 t/5 = – 18/5
⇒ t = – 18/5 Answer
Alternate Method to solve an equation
Given, 5t + 28 = 10
After transposing 28 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, 28 will become – 28 when transposed to RHS
⇒ 5t = 10 – 28
⇒ 5t = – 18
After transposing 5 to RHS, we get
When a number or digit which is in multiple in one side is transposed to other side, it goes in denominator.
Thus, here 5 becomes 1/5 after transposing to RHS
Thus, t = – 18/5 Answer
Question (1) (c) a/5 + 3 = 2
Solution
Given, a/5 + 3 = 2
After subtracting 3 from both sides, we get
a/5 + 3 – 3 = 2 – 3
⇒ a/5 = – 1
After multiplying both sides with 5 we get
⇒ a/5 × 5 = – 1 × 5
⇒ a = – 5 Answer
Alternate Method to solve an equation
Given, a/5 + 3 = 2
After transposing 3 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +3 will become –3 when transposed to RHS
⇒ a/5 = 2 – 3
⇒ a/5 = – 1
After transposing 5 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 5 is in LHS in denominator, thus, it will become in multiplication in RHS
⇒ a = –1 × 5
⇒ a = –5 Answer
Question (1)(d)q/4 + 7 = 5
Solution
Given, q/4 + 7 = 5
After subtracting 7 from both sides, we get
q/4 + 7 – 7 = 5 – 7
⇒ q/4 = – 2
After multiplying both sides with 4, we get
⇒ q/4 × 4 = – 2 × 4
⇒ q = – 8 Answer
Alternate Method to solve an equation
Given, q/4 + 7 = 5
After transposing 7 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, + 7 will become – 7 when transposed to RHS
q/4 = 5 – 7
⇒ q/4 = – 2
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
⇒ q = – 2 × 4
⇒ q = – 8 Answer
Question (1)(e) 5/2 x = – 10
Solution
After multiplying both sides with 2, we get
5/2 x × 2 = – 10 × 2
⇒ 5 x = – 20
After dividing both sides with 5, we get
⇒ 5x/5 = – 20/5
⇒ x = – 4 Answer
Alternate Method to solve an equation
Given, 5/2 x = – 10
After transposing 2 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 2 is in LHS in denominator, thus, it will become in multiplication in RHS
⇒ 5 x = – 10× 2
⇒ 5 x = – 20
After transposing 5 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 5 will become in division, i.e. goes to denominator after transposing to RHS
⇒ x = – 20/5
x = – 4 Answer
Question (1) (f)5/2 x = 25/4
Solution
Given, 5/2 x = 25/4
After multiplying both sides with 2, we get
⇒ 5/2 𝓍 × 2 = 25/4 × 2
⇒ 5 x = 50/4
After dividing both sides by 5, we get
⇒ 5 x/5 = 50/4 × 5
⇒ x = 10/4
x = 5/2 Answer
Alternate Method to solve an equation
Given, 5/2 x = 25/4
After transposing 2 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 2 is in LHS in denominator, thus, it will become in multiplication in RHS
5x = 25 × 2/4
⇒ 5 x = 50/4
After transposing 5 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 5 will become in division, i.e. goes to denominator after transposing to RHS
⇒ x = 50/4 × 5
⇒ x = 10/4
⇒ x = 5/2 Answer
Question (1) (g) 7 m + 19/2 = 13
Solution
Given, 7 m + 19/2 = 13
After subtracting 19/2 from both sides, we get
⇒ 7m + 19/2 – 19/2 = 13 – 19/2
⇒ 7 m = 26 – 19/2
⇒ 7 m = 7/2
After dividing both sides by 7, we get
⇒ 7m/7 = 7/2 × 7
⇒m = 1/2 Answer
Alternate Method to solve an equation
Given, 7 m + 19/2 = 13
After transposing 19/2 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, 19/2 will become – 19/2 when transposed to RHS
⇒ 7 m = 13 – 19/2
⇒ 7 m = 26 – 19/2
⇒ 7 m = 7/2
After transposing 7 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 7 will become in division, i.e. goes to denominator after transposing to RHS
⇒ m = 7/2 × 7
⇒ m = 1/2 Answer
Question(1) (h) 6z + 10= – 2
Solution
Given, 6z + 10 = – 2
After subtracting 10 from both sides, we get
⇒ 6z + 10 – 10 = – 2 – 10
⇒ 6z = 12
After dividing both sides by 6, we get
6z/6 = – 12/6
⇒ z = –2 Answer
Alternate Method to solve an equation
Given, 6z + 10 = – 2
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
⇒ 6z = – 2 – 10
⇒ 6z = –– ansposing 6 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 6 will become in division, i.e. goes to denominator after transposing to RHS
⇒6z/6 = – 12/6
⇒ z = – 2 Answer
Question(1) (i) 3ℓ/2 = 2/3
Solution
Given, 3ℓ/2 = 2/3
After multiplying both sides by 2, we get
3ℓ/2 × 2 = 2/3 × 2
⇒ 3 ℓ = 4/3
After dividing both sides by 3, we get
⇒ 3 ℓ/3 = 4/3 × 3
⇒ ℓ = 4/9 Answer
Alternate Method to solve an equation
Given, 3ℓ/2 = 2/3
After transposing 2 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 2 is in LHS in denominator, thus, it will become in multiplication in RHS
⇒3 ℓ = 2 × 2/3
⇒ 3ℓ = 4/3
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
⇒ℓ = 4/3 × 3
⇒ ℓ = 4/9 Answer
Question (1) (j) 2b/3 – 5 = 3
Solution
Given, 2 b/3 – 5 = 3
After adding 5 to both sides, we get
⇒ 2b/3 – 5 + 5 = 3 + 5
⇒ 2b/3 = 8
After multiplying both sides by 3, we get
⇒ 2 b/3 ×3 = 8 × 3
⇒ 2b = 24
After dividing both sides by 2, we get
⇒ 2b/2 = 24/2
⇒ b = 12 Answer
Alternate Method to solve an equation
Given, 2b/3 – 5 = 3
After transposing – 5 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, – 5 will become +5 when transposed to RHS
⇒ 2b/3 = 3 + 5
2b/3 = 8
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 is in LHS in denominator, thus, it will become in multiplication in RHS
⇒ 2b = 8 × 3
⇒ 2b = 24
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
⇒ b = 24/2
⇒ b = 12 Answer
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