If `3/4 y =6-1/3c,` then what is the value of `2x + 9/2y` ?

Explanation

To solve the equation \( \frac{3}{4}y = 6 - \frac{1}{3}c \) and find the value of \( 2c + \frac{9}{2}y \), we can follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 12.

\[ 12 \cdot \left(\frac{3}{4}y\right) = 12 \cdot \left(6 - \frac{1}{3}c\right) \]

### Step 2: Simplify both sides
Now we simplify both sides:

\[ 12 \cdot \frac{3}{4}y = 12 \cdot 6 - 12 \cdot \frac{1}{3}c \]

Calculating each term:

\[ 9y = 72 - 4c \]

### Step 3: Rearrange the equation
Now, we can rearrange the equation to isolate \( 9y + 4c \):

\[ 9y + 4c = 72 \]

### Step 4: Divide the entire equation by 2
To find the expression \( 2c + \frac{9}{2}y \), we can divide the entire equation by 2:

\[ \frac{9y}{2} + \frac{4c}{2} = \frac{72}{2} \]

This simplifies to:

\[ \frac{9}{2}y + 2c = 36 \]

### Step 5: Rearranging to find \( 2c + \frac{9}{2}y \)
Rearranging gives us:

\[ 2c + \frac{9}{2}y = 36 \]

### Conclusion
Thus, the value of \( 2c + \frac{9}{2}y \) is:

\[ \boxed{36} \]

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