What is the value of \( x \) ? \( 6.75+\frac{3}{8} x=13 \frac{1}{4} \) \( 2 \frac{7}{16} \) \( 17 \frac{1}{3} \) \( 53 \frac{1}{3} \)

To solve the equation \( 6.75+\frac{3}{8} x=13 \frac{1}{4} \), first, let's convert all the mixed numbers and decimals into improper fractions or a common format for ease of calculations. 1. Convert \( 6.75 \) to a fraction: \( 6.75 = \frac{27}{4} \). 2. Convert \( 13 \frac{1}{4} \) to an improper fraction: \( 13 \frac{1}{4} = \frac{53}{4} \). Now the equation will look like: \[ \frac{27}{4} + \frac{3}{8} x = \frac{53}{4} \] Next, subtract \( \frac{27}{4} \) from both sides: \[ \frac{3}{8} x = \frac{53}{4} - \frac{27}{4} = \frac{26}{4} = \frac{13}{2} \] Now, to isolate \( x \), multiply both sides by the reciprocal of \( \frac{3}{8} \), which is \( \frac{8}{3} \): \[ x = \frac{13}{2} \cdot \frac{8}{3} = \frac{104}{6} = \frac{52}{3} \] Converting \( \frac{52}{3} \) to a mixed number gives us \( 17 \frac{1}{3} \). Thus, the value of \( x \) is: \[ \boxed{17 \frac{1}{3}} \]