20 1/18-(х - 5 17/18)

To simplify the expression \( 20 \frac{1}{18} - (x - 5 \frac{17}{18}) \), we first convert the mixed numbers to improper fractions. 1. Convert \( 20 \frac{1}{18} \): \[ 20 \frac{1}{18} = \frac{20 \times 18 + 1}{18} = \frac{360 + 1}{18} = \frac{361}{18} \] 2. Convert \( 5 \frac{17}{18} \): \[ 5 \frac{17}{18} = \frac{5 \times 18 + 17}{18} = \frac{90 + 17}{18} = \frac{107}{18} \] Now substitute these values back into the expression: \[ \frac{361}{18} - (x - \frac{107}{18}) \] Next, simplify the equation by distributing the negative sign: \[ \frac{361}{18} - x + \frac{107}{18} \] Combine the fractional parts: \[ \frac{361 + 107}{18} - x = \frac{468}{18} - x \] Next, simplify \( \frac{468}{18} \): \[ \frac{468}{18} = 26 \] Thus, the expression simplifies to: \[ 26 - x \] So, the final simplified expression is: \[ 26 - x \]