1. **State the problem:** Solve the equation $$\frac{5x-8}{x+8} = -2$$ for $x$. 2. **Understand the formula and rules:** This is a rational equation where the variable $x$ appears in both numerator and denominator. To solve, we multiply both sides by the denominator to eliminate the fraction, but we must remember that $x \neq -8$ because the denominator cannot be zero. 3. **Multiply both sides by $x+8$ to clear the denominator:** $$\frac{5x-8}{x+8} \times (x+8) = -2 \times (x+8)$$ which simplifies to $$5x - 8 = -2(x + 8)$$ 4. **Distribute the right side:** $$5x - 8 = -2x - 16$$ 5. **Collect like terms:** Add $2x$ to both sides: $$5x + 2x - 8 = -16$$ which is $$7x - 8 = -16$$ 6. **Add 8 to both sides:** $$7x = -16 + 8$$ $$7x = -8$$ 7. **Divide both sides by 7:** $$x = \frac{-8}{7}$$ 8. **Check for restrictions:** Since $x \neq -8$, and $-\frac{8}{7} \neq -8$, the solution is valid. **Final answer:** $$x = -\frac{8}{7}$$