1. **State the problem:** Simplify the expression $-8 + 2x + 17 - 9x + 20$ and solve the equations $8x + 23 = 79$, $6x - 23 = 79$, and $8x + 15 = 79$. 2. **Simplify the expression:** Combine like terms. $$-8 + 2x + 17 - 9x + 20 = (2x - 9x) + (-8 + 17 + 20) = -7x + 29$$ 3. **Solve the first equation:** $8x + 23 = 79$ Subtract 23 from both sides: $$8x = 79 - 23$$ $$8x = 56$$ Divide both sides by 8: $$x = \frac{56}{8} = 7$$ 4. **Solve the second equation:** $6x - 23 = 79$ Add 23 to both sides: $$6x = 79 + 23$$ $$6x = 102$$ Divide both sides by 6: $$x = \frac{102}{6} = 17$$ 5. **Solve the third equation:** $8x + 15 = 79$ Subtract 15 from both sides: $$8x = 79 - 15$$ $$8x = 64$$ Divide both sides by 8: $$x = \frac{64}{8} = 8$$ **Final answers:** - Simplified expression: $-7x + 29$ - Solutions: $x=7$ for $8x + 23 = 79$, $x=17$ for $6x - 23 = 79$, and $x=8$ for $8x + 15 = 79$.