1. **State the problem:** Solve the linear equation $$7x + 23 = 79$$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 23 from both sides, then divide both sides by 7. 3. **Subtract 23 from both sides:** $$7x + 23 - 23 = 79 - 23$$ $$7x = 56$$ 4. **Divide both sides by 7:** $$\frac{\cancel{7}x}{\cancel{7}} = \frac{56}{7}$$ $$x = 8$$ 5. **Final answer:** $$x = 8$$ This means the value of $x$ that satisfies the equation is 8.