Which is the simpliferl form of the expression \( 3\left(\frac{7}{8} x+4\right)-2\left(\frac{1}{2}-\frac{4}{4} x\right) \) ? A. \( \quad-\frac{32}{f} x-\frac{1}{1} \) B. \( \frac{68 x+9}{18} x+9 \) C. \( \frac{18}{1} x+\frac{1}{2} \) D. \( 15+\frac{78}{18} x \)

We start with the expression \[ 3\left(\frac{7}{8}x+4\right)-2\left(\frac{1}{2}-\frac{4}{4}x\right). \] **Step 1. Simplify inside the parentheses.** Note that \(\frac{4}{4}=1\), so the second parentheses become: \[ \frac{1}{2}-\frac{4}{4}x=\frac{1}{2}-x. \] Thus the expression is: \[ 3\left(\frac{7}{8}x+4\right)-2\left(\frac{1}{2}-x\right). \] **Step 2. Distribute the constants.** Multiply out the terms: \[ 3\cdot\frac{7}{8}x+3\cdot4-2\cdot\frac{1}{2}+(-2)(-x). \] This gives: \[ \frac{21}{8}x+12-1+2x. \] **Step 3. Combine like terms.** Combine the constant terms: \[ 12-1=11. \] Next, combine the \(x\)-terms. Write \(2x\) as a fraction with denominator 8: \[ 2x=\frac{16}{8}x. \] Now add: \[ \frac{21}{8}x+\frac{16}{8}x=\frac{37}{8}x. \] So, the expression simplifies to: \[ \frac{37}{8}x+11. \] **Step 4. Compare with the given options.** The simplified result is \[ \frac{37}{8}x + 11, \] but none of the provided options A. \(\; -\frac{32}{f}x-\frac{1}{1}\) B. \(\frac{68x+9}{18}x+9\) C. \(\frac{18}{1}x+\frac{1}{2}\) D. \(15+\frac{78}{18}x\) matches \(\frac{37}{8}x+11\). Thus, the correct simplified form of the expression is \[ \frac{37}{8}x+11, \] which is not listed among the choices.