Comprehensive math worksheet designed for Class 8 students to practice solving linear equations in one variable through guided steps.

Problem Analysis:

The worksheet involves solving linear equations in one variable and applying them to a word problem. Let's solve each part step by step.

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Part I: Solve the following equations

#### 1. \( x + 5 = 12 \)
- Subtract 5 from both sides:
\[
x + 5 - 5 = 12 - 5
\]
\[
x = 7
\]

#### 2. \( y - 3 = 15 \)
- Add 3 to both sides:
\[
y - 3 + 3 = 15 + 3
\]
\[
y = 18
\]

#### 3. \( 5x = 20 \)
- Divide both sides by 5:
\[
\frac{5x}{5} = \frac{20}{5}
\]
\[
x = 4
\]

#### 4. \( 3x + 4 = 25 \)
- Subtract 4 from both sides:
\[
3x + 4 - 4 = 25 - 4
\]
\[
3x = 21
\]
- Divide both sides by 3:
\[
\frac{3x}{3} = \frac{21}{3}
\]
\[
x = 7
\]

#### 5. \( 2y - 3 = 24 \)
- Add 3 to both sides:
\[
2y - 3 + 3 = 24 + 3
\]
\[
2y = 27
\]
- Divide both sides by 2:
\[
\frac{2y}{2} = \frac{27}{2}
\]
\[
y = \frac{27}{2}
\]

#### 6. \( \frac{t}{3} = 10 \)
- Multiply both sides by 3:
\[
3 \cdot \frac{t}{3} = 10 \cdot 3
\]
\[
t = 30
\]

#### 7. \( 5p + 5 = 19 - 2p \)
- Add \( 2p \) to both sides:
\[
5p + 2p + 5 = 19 - 2p + 2p
\]
\[
7p + 5 = 19
\]
- Subtract 5 from both sides:
\[
7p + 5 - 5 = 19 - 5
\]
\[
7p = 14
\]
- Divide both sides by 7:
\[
\frac{7p}{7} = \frac{14}{7}
\]
\[
p = 2
\]