1. **State the problem:** Solve the equation $5x + 2 = 2x + 11$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable $x$ by performing the same operations on both sides of the equation. 3. **Subtract $2x$ from both sides:** $$5x + 2 - 2x = 2x + 11 - 2x$$ which simplifies to $$3x + 2 = 11$$ 4. **Subtract 2 from both sides:** $$3x + 2 - 2 = 11 - 2$$ which simplifies to $$3x = 9$$ 5. **Divide both sides by 3:** $$\frac{\cancel{3}x}{\cancel{3}} = \frac{9}{3}$$ which simplifies to $$x = 3$$ 6. **Final answer:** $x = 3$