\( 1 \leftarrow \) Solve and check the equation. \[ \frac{x}{8}=\frac{x}{9}-1 \] 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 \( \} \). The solution set is \( \varnothing \).

To solve the equation \( \frac{x}{8}=\frac{x}{9}-1 \), we start by eliminating the fractions. Multiply both sides by 72 (the least common multiple of 8 and 9): \[ 72 \cdot \frac{x}{8} = 72 \cdot \left(\frac{x}{9}-1\right) \] This simplifies to: \[ 9x = 8x - 72 \] Now, we isolate \( x \): \[ 9x - 8x = -72 \] \[ x = -72 \] Now, we check the solution by substituting \( x = -72 \) back into the original equation: \[ \frac{-72}{8} = \frac{-72}{9} - 1 \] \[ -9 = -8 - 1 \] \[ -9 = -9 \quad \text{(True)} \] Thus, the solution is confirmed to be \( x = -72 \). The correct choice is: A. The solution set is \( \{-72\} \). The equation takes us back to a time when fractions were treated with utmost care. In the past, mathematicians faced similar equations without the luxury of calculators, relying solely on their intellect and meticulous calculations. Picture a room filled with scrolls and ink pots, where numbers danced on parchment, and each solution felt like a small victory in the quest for knowledge! This scenario isn't just math; it's like a puzzle waiting to be solved in everyday life! Need to divide a pizza among friends? That's just a mini-equation in action! When you're finding how many slices each one should get after accounting for that one extra 'slice monster' at the party—it’s the same logical process. Understanding these connections can make math feel less daunting and more like an adventure in problem-solving!