Solve the equation. Then determine whether the eque equation \[ \frac{x+6}{2}-7=\frac{2 x-3}{3} \] What is the solution? Select the correct choice below a

Let's solve the equation step-by-step. 1. Start with the equation: \[\frac{x+6}{2}-7=\frac{2x-3}{3}\] 2. To eliminate the fractions, find a common denominator, which is 6 in this case. Multiply each term by 6: \[6\left(\frac{x+6}{2}\right) - 6 \cdot 7 = 6\left(\frac{2x-3}{3}\right)\] This simplifies to: \(3(x + 6) - 42 = 2(2x - 3)\) 3. Distribute: \(3x + 18 - 42 = 4x - 6\) which simplifies to: \(3x - 24 = 4x - 6\) 4. Now, move \(3x\) to the right side: \(-24 = x - 6\) 5. Add 6 to both sides: \(-24 + 6 = x\) \(-18 = x\) Thus, the solution is \(x = -18\). ### Verification: To check if this solution is correct, plug \(x = -18\) back into the original equation. Left side: \[ \frac{-18 + 6}{2} - 7 = \frac{-12}{2} - 7 = -6 - 7 = -13 \] Right side: \[ \frac{2(-18) - 3}{3} = \frac{-36 - 3}{3} = \frac{-39}{3} = -13 \] Both sides equal \(-13\), so the solution checks out! The correct choice would confirm the solution: \(x = -18\).