https://file.aiquickdraw.com/mathbot/file/1726872271513ok51ahbs.jpg

The equation given is:

\[
\frac{3}{4}(5f - 3) = \frac{3}{8}
\]

Let's solve for \( f \).

### Step-by-step solution:

1. **Distribute \(\frac{3}{4}\) on the left-hand side**:
   \[
   \frac{3}{4} \times 5f - \frac{3}{4} \times 3 = \frac{3}{8}
   \]
   This simplifies to:
   \[
   \frac{15f}{4} - \frac{9}{4} = \frac{3}{8}
   \]

2. **Eliminate the denominators by multiplying the entire equation by 8**:
   \[
   8 \times \left( \frac{15f}{4} - \frac{9}{4} \right) = 8 \times \frac{3}{8}
   \]
   Simplifying this gives:
   \[
   2(15f - 9) = 3
   \]
   Which simplifies to:
   \[
   30f - 18 = 3
   \]

3. **Solve for \( f \)**:
   Add 18 to both sides:
   \[
   30f = 21
   \]
   Divide both sides by 30:
   \[
   f = \frac{21}{30} = 0.7
   \]

Thus, the value of \( f \) is \( f = 0.7 \).

Would you like more details or have any questions?

Here are some related questions:
1. How would the solution change if the right-hand side were a different fraction?
2. How do you solve similar equations with different coefficients?
3. Can this equation be solved graphically? How?
4. How does multiplying by the least common denominator (LCD) help in solving fractions?
5. Can this method be applied to non-linear equations involving fractions?

**Tip:** Always check your solution by substituting the value back into the original equation to ensure it's correct.

Learn how to solve a linear equation with fractions: (3/4)(5f - 3) = 3/8. This step-by-step solution covers key algebraic concepts like the distributive property and solving equations involving fractions. Suitable for students in Grades 7-9.

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