Let's solve for $c$ step by step.

We start with the equation:

$\frac{3}{4} = \frac{1}{3} - \frac{1}{3}c$

Step 1: Move terms involving $c$ to one side

To isolate $c$, first subtract $\frac{1}{3}$ from both sides:

$\frac{3}{4} - \frac{1}{3} = -\frac{1}{3}c$

Step 2: Simplify the left side

To subtract $\frac{3}{4}$ and $\frac{1}{3}$, we need a common denominator. The least common denominator between 4 and 3 is 12. Rewrite both fractions with denominator 12:

$\frac{3}{4} = \frac{9}{12} \quad \text{and} \quad \frac{1}{3} = \frac{4}{12}$

Now subtract them:

$\frac{9}{12} - \frac{4}{12} = \frac{5}{12}$

So the equation becomes:

$\frac{5}{12} = -\frac{1}{3}c$

Step 3: Solve for $c$

Now, to solve for $c$, multiply both sides of the equation by $-3$ to eliminate the fraction on the right:

$-3 \times \frac{5}{12} = c$

$c = \frac{-3 \times 5}{12} = \frac{-15}{12}$

Step 4: Simplify the fraction

Simplify $\frac{-15}{12}$:

$\frac{-15}{12} = \frac{-5}{4}$

So, the solution is:

$c = \frac{-5}{4}$

Final Answer:

$c = \frac{-5}{4}$

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Would you like further clarification or details on any steps? Here are some related questions you might find useful:

1. How do I find a common denominator when adding or subtracting fractions?
2. What does it mean to "simplify" a fraction, and how do I do it?
3. How can I solve linear equations involving fractions more efficiently?
4. What happens when you multiply both sides of an equation by a constant?
5. How do I check the solution to an equation?

Tip: Always check your solution by substituting it back into the original equation to verify it works!