Solve the equation. \[ \frac{x+4}{2}=4-\frac{x+6}{7} \] What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). (Type an integer or a fraction.) B. The solution set is \( \{x \mid x \) is a real number \( \} \). C. The solution set is \( \varnothing \).

We start with the equation \[ \frac{x+4}{2} = 4 - \frac{x+6}{7}. \] **Step 1.** Multiply both sides by the common denominator \(14\) to eliminate the fractions: \[ 14\left(\frac{x+4}{2}\right) = 14\left(4 - \frac{x+6}{7}\right). \] **Step 2.** Simplify each term: \[ 7(x+4) = 56 - 2(x+6). \] **Step 3.** Expand the expressions: \[ 7x + 28 = 56 - 2x - 12. \] **Step 4.** Combine like terms on the right side: \[ 7x + 28 = 44 - 2x. \] **Step 5.** Add \(2x\) to both sides to get the \(x\)-terms together: \[ 7x + 2x + 28 = 44, \] \[ 9x + 28 = 44. \] **Step 6.** Subtract \(28\) from both sides: \[ 9x = 44 - 28, \] \[ 9x = 16. \] **Step 7.** Divide both sides by \(9\): \[ x = \frac{16}{9}. \] Thus, the solution set is \[ \left\{\frac{16}{9}\right\}. \] Select choice A: The solution set is \( \left\{\frac{16}{9}\right\} \).