Which value of x makes the equation `8/5(x+(33)/(12))=16` true ?

Options

A. `7.25`
B. `8.75`
C. `12.75`
D. `13.25`

Explanation

To solve the equation \( \frac{8}{5}(x + \frac{33}{12}) = 16 \), we will follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by \( 5 \) to eliminate the fraction on the left side:

\[ 5 \cdot \frac{8}{5}(x + \frac{33}{12}) = 5 \cdot 16 \]

This simplifies to:

\[ 8(x + \frac{33}{12}) = 80 \]

### Step 2: Distribute the 8
Now, distribute \( 8 \) on the left side:

\[ 8x + 8 \cdot \frac{33}{12} = 80 \]

Calculating \( 8 \cdot \frac{33}{12} \):

\[ 8 \cdot \frac{33}{12} = \frac{264}{12} = 22 \]

So, the equation becomes:

\[ 8x + 22 = 80 \]

### Step 3: Isolate the term with x
Subtract \( 22 \) from both sides to isolate the term with \( x \):

\[ 8x = 80 - 22 \]

This simplifies to:

\[ 8x = 58 \]

### Step 4: Solve for x
Now, divide both sides by \( 8 \):

\[ x = \frac{58}{8} \]

This can be simplified to:

\[ x = \frac{29}{4} = 7.25 \]

### Final Answer
Thus, the value of \( x \) that makes the equation true is:

\[ \boxed{7.25} \]

---