Solve the equation. \[ h-7 \frac{5}{6}=5 \frac{1}{2} \] \( h=\square \) (Type a whole number, fraction, or mixed number.)

To solve the equation \( h - 7 \frac{5}{6} = 5 \frac{1}{2} \), first convert the mixed numbers into improper fractions. For \( 7 \frac{5}{6} \): \[ 7 \frac{5}{6} = \frac{7 \times 6 + 5}{6} = \frac{42 + 5}{6} = \frac{47}{6} \] For \( 5 \frac{1}{2} \): \[ 5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \] Now we rewrite the equation: \[ h - \frac{47}{6} = \frac{11}{2} \] To eliminate the fraction, we can find a common denominator, which is 6 in this case. Rewrite \( \frac{11}{2} \) as: \[ \frac{11}{2} = \frac{11 \times 3}{2 \times 3} = \frac{33}{6} \] Now, the equation becomes: \[ h - \frac{47}{6} = \frac{33}{6} \] Add \( \frac{47}{6} \) to both sides: \[ h = \frac{33}{6} + \frac{47}{6} = \frac{33 + 47}{6} = \frac{80}{6} \] Now simplify \( \frac{80}{6} \): \[ h = \frac{40}{3} \] This can also be represented as a mixed number: \[ h = 13 \frac{1}{3} \] So, \( h = 13 \frac{1}{3} \).