Simple equations are puzzles where you need to find the value of an unknown variable. They involve variables (like n, p, etc.) and are equal to some value. The goal is to find these variable values.
Class 7 Maths Exercise 4.2 Simple Equations
Note: Whatever you do to one side of the equation, you must do to the other side.
Example 1: Solve 3n + 7 = 25
Isolate the variable: We want to get n by itself.
Subtract 7 from both sides: 3n + 7 – 7 = 25 – 7.
Simplify: 3n = 18.
Solve for the variable: Divide both sides by 3 to get n.
3n + 7 = 25
3n = 25 – 7 (taking 7 to RHS)
3n = 18
Divide by 3: 3n/3 = 18/3.
Simplify: n = 6.
Example 2: Solve 2p – 1 = 23
Isolate the variable: We want to get p by itself.
Add 1 to both sides: 2p – 1 + 1 = 23 + 1.
Simplify: 2p = 24.
Solve for the variable: Divide both sides by 2 to find p.
2p – 1 = 23
2p = 23 + 1 (taking -1 to RHS)
2p = 24
Divide by 2: 2p/2 = 24/2.
Simplify: p = 12.
Checking Your Solution
It’s good practice to check if your solution is correct. Plug the value back into the original equation.
For p = 12:
Original equation: 2p – 1 = 23.
Substitute p: 2 x 12 – 1 = 23.
Simplify: 24 – 1 = 23.
As 23 = 23, our solution p = 12 is correct!
Remember, solving equations is a game of balancing. Each step to find the variable’s value must keep the equation balanced.
NCERT Solutions for Class 7 Maths Exercise 4.2 Chapter 4 Simple Equations
1. Give first the step you will use to separate the variable and then solve the equation:
(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
Solutions
(a) x – 1 = 0
First Step: Add 1 to both sides
x – 1 + 1 = 0 + 1
x = 1
(b) x + 1 = 0
First Step: Subtract 1 from both sides
x + 1 – 1 = 0 – 1
x = -1
(c) x – 1 = 5
First Step: Add 1 to both sides
x – 1 + 1 = 5 + 1
x = 6
(d) x + 6 = 2
First Step: Subtract 6 from both sides
x + 6 – 6 = 2 – 6
x = -4
(e) y – 4 = –7
First Step: Add 4 to both sides
y – 4 + 4 = –7 + 4
y = -3
(f) y – 4 = 4
First Step: Add 4 to both sides
y – 4 + 4 = 4 + 4
y = 8
(g) y + 4 = 4
First Step: Subtract 4 from both sides
y + 4 – 4 = 4 – 4
y = 0
(h) y + 4 = –4
First Step: Subtract 4 from both sides
y + 4 – 4 = –4 – 4
y = -8
2. Give first the step you will use to separate the variable and then solve the equation:
(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
Solutions
(a) 3l = 42
First Step: Divide both sides by 3
3l / 3 = 42 / 3
l = 14
(b) b / 2 = 6
First Step: Multiply both sides by 2
b / 2 * 2 = 6 * 2
b = 12
(c) p / 7 = 4
First Step: Multiply both sides by 7
p / 7 * 7 = 4 * 7
p = 28
(d) 4x = 25
First Step: Divide both sides by 4
4x / 4 = 25 / 4
x = 6.25
(e) 8y = 36
First Step: Divide both sides by 8
8y / 8 = 36 / 8
y = 4.5
(f) z / 3 = 5 / 4
First Step: Multiply both sides by 3
z / 3 * 3 = 5 / 4 * 3
z = 15 / 4
= 3.75
(g) a / 5 = 7 / 15
First Step: Multiply both sides by 5
a / 5 * 5 = 7 / 15 * 5
a = 7 / 3
= 2.33 (approx)
(h) 20t = –10
First Step: Divide both sides by 20
20t / 20 = –10 / 20
t = –0.5
3. Give the steps you will use to separate the variable and then solve the equation:
(a) 3n – 2 = 46 (b) 5m + 7 = 17 (c) 20p/3 = 40 (d) 3p/10 = 6
Solutions
(a) 3n – 2 = 46
First Step: Add 2 to both sides
3n – 2 + 2 = 46 + 2
3n = 48
Second Step: Divide both sides by 3
3n / 3 = 48 / 3
n = 16
(b) 5m + 7 = 17
First Step: Subtract 7 from both sides
5m + 7 – 7 = 17 – 7
5m = 10
Second Step: Divide both sides by 5
5m / 5 = 10 / 5
m = 2
(c) 20p / 3 = 40
First Step: Multiply both sides by 3
20p / 3 * 3 = 40 * 3
20p = 120
Second Step: Divide both sides by 20
20p / 20 = 120 / 20
p = 6
(d) 3p / 10 = 6
First Step: Multiply both sides by 10
3p / 10 * 10 = 6 * 10
3p = 60
Second Step: Divide both sides by 3
3p / 3 = 60 / 3
p = 20
4. Solve the following equations:
(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
Solutions
(a) 10p = 100
Divide both sides by 10
10p / 10 = 100 / 10
p = 10
(b) 10p + 10 = 100
First Step: Subtract 10 from both sides
10p + 10 – 10 = 100 – 10
10p = 90
Second Step: Divide both sides by 10
10p / 10 = 90 / 10
p = 9
(c) p / 4 = 5
Multiply both sides by 4
p / 4 * 4 = 5 * 4
p = 20
(d) –p / 3 = 5
Multiply both sides by -3
–p / 3 * -3 = 5 * -3
p = -15
(e) 3p / 4 = 6
Multiply both sides by 4
3p / 4 * 4 = 6 * 4
3p = 24
Divide both sides by 3
3p / 3 = 24 / 3
p = 8
(f) 3s = –9
Divide both sides by 3
3s / 3 = –9 / 3
s = -3
(g) 3s + 12 = 0
First Step: Subtract 12 from both sides
3s + 12 – 12 = 0 – 12
3s = -12
Second Step: Divide both sides by 3
3s / 3 = -12 / 3
s = -4
(h) 3s = 0
Divide both sides by 3
3s / 3 = 0 / 3
s = 0
(i) 2q = 6
Divide both sides by 2
2q / 2 = 6 / 2
q = 3
(j) 2q – 6 = 0
First Step: Add 6 to both sides
2q – 6 + 6 = 0 + 6
2q = 6
Second Step: Divide both sides by 2
2q / 2 = 6 / 2
q = 3
(k) 2q + 6 = 0
First Step: Subtract 6 from both sides
2q + 6 – 6 = 0 – 6
2q = -6
Second Step: Divide both sides by 2
2q / 2 = -6 / 2
q = -3
(l) 2q + 6 = 12
First Step: Subtract 6 from both sides
2q + 6 – 6 = 12 – 6
2q = 6
Second Step: Divide both sides by 2
2q / 2 = 6 / 2
q = 3
