NCERT Exercise 4.2 Solution
Simple Equations 7th Math
NCERT Exercise 4.2 Solution
Question (1) Give first step you will use to separate the variable and then solve the equation:
Question (1) (a) x – 1 = 0
Solution
Given, x – 1 = 0
After adding 1 to both sides, i.e. to LHS and RHS, we get
x – 1 + 1 = 0 + 1
⇒ x = 1
Thus, add 1 to both sides, x = 1 Answer
Alternate Method to solve an equation
Given, x – 1 = 0
After transposing – 1 to RHS,
[When a digit or variable is transposed to other side, its sign changes]
Thus, – 1 will become +1 when transposed to RHS
Thus, x = 0 + 1
⇒ x = 1 Answer
Question (1) (b) x + 1 = 0
Solution
Given, x + 1 = 0
After subtracting 1 to both sides, i.e. LHS and RHS, we get
x + 1 – 1 = 0 – 1
⇒ x = – 1
Thus, subtract 1 to both sides, x = – 1 Answer
Alternate Method to solve an equation
Given, x + 1 = 0
After transposing 1 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +1 will become – 1 when transposed to RHS
Thus, x = 0 – 1
⇒ x = – 1
Thus, x = – 1 Answer
Question (1) (c) x – 1 = 5
Solution
Given, x – 1 = 5
After adding 1 to both sides, i.e. to LHS and RHS, we get
x – 1 + 1 = 5 + 1
⇒ x = 6
Thus, Add 1 to both sides, x = 6 Answer
Alternate Method to solve an equation
Given, x – 1 = 5
After transposing – 1 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, – 1 will become +1, when transposed to RHS
Thus, x = 5 + 1
⇒ x = 6
Thus, x = 6 Answer
(d) x + 6 = 2
Solution
Given, x + 6 = 2
After subtracting 6 to both sides, i.e. LHS and RHS, we get
x + 6 – 6 = 2 – 6
⇒ x = – 4
Thus, subtract 6 to both sides, x = – 4 Answer
Alternate Method to solve an equation
Given, x + 6 = 2
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
Thus, x = 2 – 6
⇒ x = – 4
Thus, x = – 4 Answer
Question (1) (e) y – 4 = – 7
Solution
Given, y – 4 = – 7
After adding 4 to both sides, i.e. to LHS and RHS, we get
y – 4 + 4 = – 7 + 4
⇒ y = – 3
Thus, Add 4 to both sides, y = – 3 Answer
Alternate method to solve an equation
Given, y – 4 = – 7
After transposing – 4 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, – 4 will become +4 when transposed to RHS
Thus, y = – 7 + 4
⇒ y = – 3
Thus, transpose – 4 to RHS, y = – 3 Answer
Question (1) (f) y – 4 = 4
Solution
Given, y – 4 = 4
After adding 4 to both sides, i.e. to LHS and RHS, we get
y – 4 + 4 = 4 + 4
⇒ y = 8
Thus, Add 4 to both sides, y = 8 Answer
Alternate method to solve an equation
Given, y – 4 = 4
After transposing – 4 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, – 4 will become +4 when transposed to RHS
Thus, y = 4 + 4
⇒ y = 8
Thus, transpose – 4 to RHS, y = 8 Answer
Question (1) (g) y + 4 = 4
Solution
Given, y + 4 = 4
After subtracting 4 to both sides, i.e. to LHS and RHS, we get
⇒ y + 4 – 4 = 4 – 4
⇒ y = 0
Thus, Subtract 4 to both sides, y = 0 Answer
Alternate method to solve an equation
Given, y + 4 = 4
After transposing 4 to RHS, we get
[When a digit or variable is transposed to other side, its sign changes]
Thus, 4 will become – 4 when transposed to RHS
y = 4 – 4
⇒ y = 0
Thus, transpose 4 to RHS, y = 0 Answer
Question (1) (h) y + 4 = – 4
Solution
Given, y + 4 = – 4
After subtracting 4 to both sides, i.e. to LHS and RHS, we get
⇒ y + 4 – 4 = – 4 – 4
⇒ y = – 8
Thus, Subtract 4 to both sides, y = – 8 Answer
Alternate method to solve an equation
Given, y + 4 = – 4
After transposing 4 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, 4 will become – 4 when transposed to RHS
Thus, y = – 4 – 4
⇒ y = – 8
Thus, transpose 4 to RHS, y = – 8 Answer
Question (2) Give first the step you will use to separate the variable and then solve the equation.
Question (2) (a)3 ℓ = 42
Solution
Given, 3 ℓ = 42
After dividing both sides by 3, i.e. to LHS and RHS, we get
3 ℓ/3 = 42/3
⇒ ℓ = 14
Thus, divide both sides by 3, l = 14 Answer
Alternate method to solve an equation
Given, 3 ℓ = 42
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 after transposing to RHS
Thus, ℓ = 42/3
⇒ℓ = 14
Thus, transpose 3 to RHS, ℓ = 14 Answer
Question(2) (b) b/2 = 6
Solution
Given, b/2 = 6
After multiplying both sides by 2, we get
b/2 × 2 = 6 ×2
⇒ b = 12
Thus, multiplying both sides by 2, b = 12 Answer
Alternate method to solve an equation
Given, b/2 = 6
After trasnsposing 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
Thus, b = 6 × 2
⇒ b = 12
Thus, transposing 2 to RSH, b = 12 Answer
Quedtion (2) (c) p/7 = 4
Solution
Given,p/7 = 4
After multiplying both sides with 7, we get
p/7 × 7 = 4 ×7
⇒ p = 28
Thus, multiply both sides with 7, p = 28 Answer
Alternate method to solve an equation
Given, p/7 = 4
After trasnsposing 7 to RHS.
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 7 is in LHS in denominator, thus, it will become in multiplication in RHS
Thus, p = 4 × 7
⇒ p = 28
Thus, transposing 7 to RHS, p = 28 Answer
(d) 4 x = 25
Solution
Given, 4 x = 25
After dividing both sides by 4, we get
4 x/4 = 25/4
⇒ x = 25/4
Thus, dividing both sides by 4, x = 25/4 Answer
Alternate method to solve an equation
Given, 4 x = 25
After transposing 4 to RHS,
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 4 will become in division after transposing to RHS
Thus, x = 25/4
Thus, 4 is transposed to RHS, x = 25/4 Answer
Question (2)(e) 8y = 36
Solution
Given, 8 y = 36
After dividing both sides by 8, we get
8y/8 = 36/8
⇒ y = 9/2
Thus, dividing both sides by 8, y = 9/2 Answer
Alternate method to solve an equation
Given, 8y = 36
After transposing 8 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 8 will become in division after transposing to RHS
Thus, y = 36/8
⇒y = 9/2
Thus, transposing 8 to RHS, y = 9/2 Answer
Question (2) (f) z/3 = 5/4
Solution
Given, z/3 = 5/4
After multiplying both sides with 3 we get
z/3 × 3 = 5/4 × 3
⇒ z = 15/4
Thus, multiplying both sides by 3, z = 15/4 Answer
Alternate method to solve an equation
Given, z/3 = 5/4
After trasnsposing 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
Thus, z = 5/4 × 3
⇒ z = 5 × 3/4
⇒ z = 15/4
Thus, transposing 3 to RHS, z = 15/4 Answer
Quedtion (2) (g) a/5 = 7/15
Solution
Given, a/5 = 7/15
After multiplying both sides with 5, we get
a/5 × 5= 7/15 × 5
⇒ a = 7/3
Thus, multiplying both sides by 5, a = 7/3 Answer
Alternate method to solve an equation
Given, a/5 = 7/15
After trasnsposing 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
Thus, a = 7/15 × 5
⇒ a = 7/3
Thus, transposing 5 to RHS, a = 7/3 Answer
Question (2) (h) 20 t = – 10
Solution
Given, 20 t = – 10
After dividing both sides with 20, we get
20 t/20 = – 10/20
⇒ t = – 1/2
Thus, multiplying both sides with 20, t = 1/2 Answer
Alternate method to solve an equation
Given, 20 t = – 10
After transposing 20 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 20 will become in division, i.e. goes to denominator after transposing to RHS
Thus, t = – 10/20
⇒ t = – 1/2
Thus, transposing 20 to RHS, t = – 1/2 Answer
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