1. **State the problem:** Solve for $x$ in the equation $7x - 23 = 2x + 17$. 2. **Write down the equation:** $$7x - 23 = 2x + 17$$ 3. **Isolate the variable terms on one side:** Subtract $2x$ from both sides: $$7x - \cancel{2x} - 23 = \cancel{2x} + 17 - 2x$$ which simplifies to $$5x - 23 = 17$$ 4. **Isolate the constant term on the other side:** Add $23$ to both sides: $$5x - 23 + 23 = 17 + 23$$ which simplifies to $$5x = 40$$ 5. **Solve for $x$ by dividing both sides by 5:** $$\frac{5x}{\cancel{5}} = \frac{40}{\cancel{5}}$$ which simplifies to $$x = 8$$ 6. **Final answer:** $$\boxed{8}$$