Let's solve the equation step by step:

\[
\frac{3}{8}f + \frac{1}{2} = 6\left(\frac{1}{16}f - 3\right)
\]

### Step 1: Distribute the 6 on the right side of the equation

\[
\frac{3}{8}f + \frac{1}{2} = 6 \times \frac{1}{16}f - 6 \times 3
\]

\[
\frac{3}{8}f + \frac{1}{2} = \frac{6}{16}f - 18
\]

### Step 2: Simplify the fraction \(\frac{6}{16}\) on the right side

\[
\frac{3}{8}f + \frac{1}{2} = \frac{3}{8}f - 18
\]

### Step 3: Subtract \(\frac{3}{8}f\) from both sides

\[
\frac{1}{2} = -18
\]

### Step 4: Observe the result

The equation \(\frac{1}{2} = -18\) is a contradiction, meaning it is not true. Therefore, the original equation has **no solution**.

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. How do you solve equations with variables on both sides?
2. What are the steps to solving a linear equation?
3. What does it mean when an equation has no solution?
4. How do you check if an equation is an identity?
5. How can you solve a system of linear equations?

**Tip:** When you encounter a contradiction in a linear equation, it usually means there is no solution for the given equation.

Learn how to solve the equation \(\frac{3}{8}f + \frac{1}{2} = 6(\frac{1}{16}f - 3)\) step-by-step. This problem involves equations with fractions and the distributive property, suitable for Grades 7-9 students.

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