1. **State the problem:** Solve for $x$ in the equation $$\frac{8x}{3} = \frac{x}{5} - 74$$. 2. **Write down the equation:** $$\frac{8x}{3} = \frac{x}{5} - 74$$. 3. **Eliminate the fractions by multiplying both sides by the least common denominator (LCD), which is 15:** $$15 \times \frac{8x}{3} = 15 \times \left(\frac{x}{5} - 74\right)$$ 4. **Simplify each term:** $$15 \times \frac{8x}{3} = \cancel{15} \times \frac{8x}{\cancel{3}} = 5 \times 8x = 40x$$ $$15 \times \frac{x}{5} = \cancel{15} \times \frac{x}{\cancel{5}} = 3x$$ $$15 \times (-74) = -1110$$ So the equation becomes: $$40x = 3x - 1110$$ 5. **Bring all terms involving $x$ to one side:** $$40x - 3x = -1110$$ $$37x = -1110$$ 6. **Solve for $x$ by dividing both sides by 37:** $$x = \frac{-1110}{37}$$ 7. **Simplify the fraction if possible:** 37 is a prime number and does not divide 1110 evenly, so the fraction stays as is. **Final answer:** $$x = -\frac{1110}{37}$$