CBSE Clas 7 Maths Worksheet - Simple Equations PDF | PDF - Free Printable

Let's solve the problems step by step from the worksheet.

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Part I: Solve the following equations

We will solve each equation one by one.

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#### 1. $ 3x - 14 = 16 $

Add 14 to both sides:
$$
3x = 16 + 14 = 30
$$
Divide by 3:
$$
x = \frac{30}{3} = 10
$$

✔ Answer: $ x = 10 $

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#### 2. $ 4(2x + 1) = 36 $

Expand:
$$
8x + 4 = 36
$$
Subtract 4:
$$
8x = 32
$$
Divide by 8:
$$
x = 4
$$

✔ Answer: $ x = 4 $

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#### 3. $ 3(2x - 1) + 5 = 14 $

Expand:
$$
6x - 3 + 5 = 14 \Rightarrow 6x + 2 = 14
$$
Subtract 2:
$$
6x = 12
$$
Divide by 6:
$$
x = 2
$$

✔ Answer: $ x = 2 $

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#### 4. $ 2y - (7 - 5y) - 21 = 0 $

Simplify inside parentheses:
$$
2y - 7 + 5y - 21 = 0 \Rightarrow 7y - 28 = 0
$$
Add 28:
$$
7y = 28
$$
Divide by 7:
$$
y = 4
$$

✔ Answer: $ y = 4 $

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#### 5. $ 2(f - 2) + 3(4f - 1) = 7 $

Expand:
$$
2f - 4 + 12f - 3 = 7 \Rightarrow 14f - 7 = 7
$$
Add 7:
$$
14f = 14
$$
Divide by 14:
$$
f = 1
$$

✔ Answer: $ f = 1 $

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#### 6. $ 3m + 2(m + 2) = 20 - (2m - 5) $

Left side:
$$
3m + 2m + 4 = 5m + 4
$$

Right side:
$$
20 - 2m + 5 = 25 - 2m
$$

So:
$$
5m + 4 = 25 - 2m
$$
Add $ 2m $:
$$
7m + 4 = 25
$$
Subtract 4:
$$
7m = 21
$$
Divide by 7:
$$
m = 3
$$

✔ Answer: $ m = 3 $

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#### 7. $ 3a - a(2a - 5) = a(a + 3) - 8 $

Left side:
$$
3a - 2a^2 + 5a = 8a - 2a^2
$$

Right side:
$$
a^2 + 3a - 8
$$

Now:
$$
8a - 2a^2 = a^2 + 3a - 8
$$

Bring all terms to one side:
$$
-2a^2 - a^2 + 8a - 3a + 8 = 0 \Rightarrow -3a^2 + 5a + 8 = 0
$$

Multiply by -1:
$$
3a^2 - 5a - 8 = 0
$$

Use quadratic formula:
$$
a = \frac{5 \pm \sqrt{(-5)^2 - 4(3)(-8)}}{2(3)} = \frac{5 \pm \sqrt{25 + 96}}{6} = \frac{5 \pm \sqrt{121}}{6}
$$
$$
\sqrt{121} = 11 \Rightarrow a = \frac{5 \pm 11}{6}
$$

So:
- $ a = \frac{16}{6} = \frac{8}{3} $
- $ a = \frac{-6}{6} = -1 $

✔ Answers: $ a = \frac{8}{3} $ or $ a = -1 $

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#### 8. $ 5(3x - 3) - 3(3x - 7) = 12 $

Expand:
$$
15x - 15 - 9x + 21 = 12 \Rightarrow 6x + 6 = 12
$$
Subtract 6:
$$
6x = 6 \Rightarrow x = 1
$$

✔ Answer: $ x = 1 $

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#### 9. $ 2(5y - 3) - 4 = 20 $

Expand:
$$
10y - 6 - 4 = 20 \Rightarrow 10y - 10 = 20
$$
Add 10:
$$
10y = 30 \Rightarrow y = 3
$$

✔ Answer: $ y = 3 $

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#### 10. $ 3(x - \frac{1}{3}) = 2(2x - 6) $

Left:
$$
3x - 1
$$

Right:
$$
4x - 12
$$

So:
$$
3x - 1 = 4x - 12
$$
Subtract $ 3x $:
$$
-1 = x - 12
$$
Add 12:
$$
x = 11
$$

✔ Answer: $ x = 11 $

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Optional Problems (11–20)

We'll solve a few of them as examples.

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#### 11. $ \frac{a + 9}{2} = 10 $

Multiply both sides by 2:
$$
a + 9 = 20
\Rightarrow a = 11
$$

✔ Answer: $ a = 11 $

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#### 12. $ \frac{b + 1}{2} = 1 $

Multiply by 2:
$$
b + 1 = 2 \Rightarrow b = 1
$$

✔ Answer: $ b = 1 $

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#### 13. $ \frac{2x + 5}{3} = 3x - 10 $

Multiply both sides by 3:
$$
2x + 5 = 9x - 30
$$
Subtract $ 2x $:
$$
5 = 7x - 30
$$
Add 30:
$$
35 = 7x \Rightarrow x = 5
$$

✔ Answer: $ x = 5 $

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#### 14. $ \frac{3(d - 2)}{9} + 5 = 7 $

Simplify:
$$
\frac{d - 2}{3} + 5 = 7
$$
Subtract 5:
$$
\frac{d - 2}{3} = 2
$$
Multiply by 3:
$$
d - 2 = 6 \Rightarrow d = 8
$$

✔ Answer: $ d = 8 $

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#### 15. $ \frac{3x + 2}{4} = \frac{x + 5}{8} $

Multiply both sides by 8:
$$
2(3x + 2) = x + 5 \Rightarrow 6x + 4 = x + 5
$$
Subtract $ x $:
$$
5x + 4 = 5
$$
Subtract 4:
$$
5x = 1 \Rightarrow x = \frac{1}{5}
$$

✔ Answer: $ x = \frac{1}{5} $

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#### 16. $ 15y - \frac{4}{5} = \frac{1}{5} $

Add $ \frac{4}{5} $:
$$
15y = \frac{1}{5} + \frac{4}{5} = 1
\Rightarrow y = \frac{1}{15}
$$

✔ Answer: $ y = \frac{1}{15} $

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#### 17. $ \frac{2d + 6}{9} + 10 = 14 $

Subtract 10:
$$
\frac{2d + 6}{9} = 4
$$
Multiply by 9:
$$
2d + 6 = 36 \Rightarrow 2d = 30 \Rightarrow d = 15
$$

✔ Answer: $ d = 15 $

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#### 18. $ \frac{d - 1}{3} - \frac{d - 2}{4} = 1 $

LCM of 3 and 4 is 12. Multiply both sides by 12:

$$
12 \left( \frac{d - 1}{3} - \frac{d - 2}{4} \right) = 12 \cdot 1
\Rightarrow 4(d - 1) - 3(d - 2) = 12
$$

Expand:
$$
4d - 4 - 3d + 6 = 12 \Rightarrow d + 2 = 12 \Rightarrow d = 10
$$

✔ Answer: $ d = 10 $

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#### 19. $ \frac{2x}{5} - 1 = \frac{5x + 10}{6} $

Multiply both sides by 30 (LCM of 5 and 6):

$$
30 \left( \frac{2x}{5} - 1 \right) = 30 \left( \frac{5x + 10}{6} \right)
\Rightarrow 6(2x) - 30 = 5(5x + 10)
\Rightarrow 12x - 30 = 25x + 50
$$

Subtract $ 12x $:
$$
-30 = 13x + 50
\Rightarrow -80 = 13x \Rightarrow x = -\frac{80}{13}
$$

✔ Answer: $ x = -\frac{80}{13} $

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#### 20. $ \frac{4m + 2}{6m + 10} = \frac{1}{2} $

Cross-multiply:
$$
2(4m + 2) = 1(6m + 10)
\Rightarrow 8m + 4 = 6m + 10
\Rightarrow 2m = 6 \Rightarrow m = 3
$$

✔ Answer: $ m = 3 $

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Part II: Write equations and solve

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#### 1. The sum of a number and 12 is 27

Let the number be $ x $. Then:
$$
x + 12 = 27 \Rightarrow x = 27 - 12 = 15
$$

✔ Answer: $ x = 15 $

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#### 2. The product of a number and 7 is 91

Let the number be $ x $:
$$
7x = 91 \Rightarrow x = \frac{91}{7} = 13
$$

✔ Answer: $ x = 13 $

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#### 3. Half of a number is 19

Let the number be $ x $:
$$
\frac{1}{2}x = 19 \Rightarrow x = 38
$$

✔ Answer: $ x = 38 $

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#### 4. Eight times a number is 120

Let the number be $ x $:
$$
8x = 120 \Rightarrow x = 15
$$

✔ Answer: $ x = 15 $

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#### 5. Three times a number plus 10 is 97

Let the number be $ x $:
$$
3x + 10 = 97 \Rightarrow 3x = 87 \Rightarrow x = 29
$$

✔ Answer: $ x = 29 $

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✔ Final Answers Summary:

#### Part I:
1. $ x = 10 $
2. $ x = 4 $
3. $ x = 2 $
4. $ y = 4 $
5. $ f = 1 $
6. $ m = 3 $
7. $ a = \frac{8}{3} $ or $ a = -1 $
8. $ x = 1 $
9. $ y = 3 $
10. $ x = 11 $
11. $ a = 11 $
12. $ b = 1 $
13. $ x = 5 $
14. $ d = 8 $
15. $ x = \frac{1}{5} $
16. $ y = \frac{1}{15} $
17. $ d = 15 $
18. $ d = 10 $
19. $ x = -\frac{80}{13} $
20. $ m = 3 $

#### Part II:
1. $ x = 15 $
2. $ x = 13 $
3. $ x = 38 $
4. $ x = 15 $
5. $ x = 29 $

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