We need to solve for \( x \) in the equation:

\[
\frac{3}{5} + \frac{13}{20} + x = 75
\]

### Step 1: Find a common denominator for the fractions
The denominators are 5 and 20. The least common denominator (LCD) is 20.

- Convert \( \frac{3}{5} \) to have a denominator of 20:
  \[
  \frac{3}{5} = \frac{12}{20}
  \]

### Step 2: Add the fractions
Now we add the two fractions:
\[
\frac{12}{20} + \frac{13}{20} = \frac{25}{20} = 1.25
\]

### Step 3: Substitute the sum of the fractions back into the equation
Now, the equation becomes:
\[
1.25 + x = 75
\]

### Step 4: Solve for \( x \)
Subtract 1.25 from both sides:
\[
x = 75 - 1.25
\]
\[
x = 73.75
\]

Thus, \( x = 73.75 \).

---

Would you like more details or have any questions? Here are some related questions for practice:

1. Solve: \( \frac{4}{7} + \frac{5}{14} + y = 10 \)
2. Solve: \( \frac{7}{8} + \frac{3}{4} + z = 20 \)
3. Simplify: \( \frac{5}{6} + \frac{7}{12} \)
4. Solve for \( x \): \( x + \frac{1}{3} = 9 \)
5. Convert \( \frac{9}{15} \) to a decimal.

**Tip:** When adding fractions, always find the least common denominator before combining!

This guide provides a step-by-step solution for solving the equation 3/5 + 13/20 + x = 75. It demonstrates how to find a common denominator to add fractions and solve a linear equation. Ideal for students in Grades 6-8 learning algebraic concepts and fraction addition.

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