Part 1 of 2 Sther than a no solution set, use interval notation to express the solution set and then graph the solution set on a number \[ \frac{x-16}{6} \geq \frac{x-8}{9}+\frac{7}{18} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is (Type your answer using interval notation.)

To solve the inequality \(\frac{x-16}{6} \geq \frac{x-8}{9}+\frac{7}{18}\), we first find a common denominator for all terms. The least common multiple of 6, 9, and 18 is 18. Rewriting the inequality with that in mind gives: \[ \frac{3(x-16)}{18} \geq \frac{2(x-8)}{18} + \frac{7}{18} \] Now, multiply everything by 18 to eliminate the denominators (remember that multiplying by a positive number keeps the direction of the inequality the same): \[ 3(x-16) \geq 2(x-8) + 7 \] Distributing gives: \[ 3x - 48 \geq 2x - 16 + 7 \] Combining the right-hand side, we get: \[ 3x - 48 \geq 2x - 9 \] Subtracting \(2x\) from both sides, we find: \[ x - 48 \geq -9 \] Adding 48 to both sides leads us to: \[ x \geq 39 \] Thus, the solution set in interval notation is \([39, \infty)\). Now, to graph this solution, you would draw a number line, mark a solid dot above 39 (indicating that 39 is included), and shade everything to the right to represent all numbers greater than or equal to 39.