1. **State the problem:** Solve the linear equation $2x + 5 = 17$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 5 from both sides, then divide both sides by 2. 3. **Subtract 5 from both sides:** $$2x + 5 - 5 = 17 - 5$$ $$2x = 12$$ 4. **Divide both sides by 2:** $$\frac{\cancel{2}x}{\cancel{2}} = \frac{12}{2}$$ $$x = 6$$ 5. **Final answer:** $x = 6$. This means the value of $x$ that satisfies the equation is 6.