Solve and check the linear equation. \( 8(x-9)-9(x-8)=x+8-(x-6) \) 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 \( \} \). B. The solution set is \( \{x \mid x \) is a real number\}. C. The solution set is \( \varnothing \).

We start with the equation:   8(x – 9) – 9(x – 8) = x + 8 – (x – 6). Step 1. Distribute on both sides.  • Left side: 8(x – 9) = 8x – 72, and 9(x – 8) = 9x – 72.   So, 8x – 72 – 9x + 72 = (8x – 9x) + (–72 + 72) = –x.  • Right side: x + 8 – (x – 6) = x + 8 – x + 6 = 14. Step 2. Write the simplified equation.   –x = 14. Step 3. Solve for x.  Multiply both sides by –1:   x = –14. Step 4. Check the solution by substituting x = –14 into the original equation.  • LHS: 8(–14 – 9) – 9(–14 – 8)   = 8(–23) – 9(–22)   = –184 + 198   = 14.  • RHS: (–14) + 8 – ((–14) – 6)   = –14 + 8 – (–20)   = –6 + 20   = 14. Since the left-hand side equals the right-hand side, the solution checks out. Thus, the unique solution is x = –14, so the solution set is { –14 }. The correct choice is: A. The solution set is { –14 }.