1. **State the problem:** Solve the linear equation $2x + 5 = 9$ for $x$. 2. **Write the 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. **Step-by-step solution:** 1. Start with the equation: $$2x + 5 = 9$$ 2. Subtract 5 from both sides: $$2x + 5 - 5 = 9 - 5$$ $$2x = 4$$ 3. Divide both sides by 2 to isolate $x$: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{4}{2}$$ $$x = 2$$ 4. **Final answer:** $$x = 2$$ This means the value of $x$ that satisfies the equation is 2.