1. **State the problem:** Solve the equation $x + \frac{x}{4} = 2$ for $x$. 2. **Formula and rules:** To solve linear equations, combine like terms and isolate the variable. 3. **Combine like terms:** $$x + \frac{x}{4} = \frac{4x}{4} + \frac{x}{4} = \frac{5x}{4}$$ 4. **Rewrite the equation:** $$\frac{5x}{4} = 2$$ 5. **Isolate $x$ by multiplying both sides by 4:** $$4 \times \frac{5x}{4} = 4 \times 2$$ 6. **Cancel common factors:** $$\cancel{4} \times \frac{5x}{\cancel{4}} = 8$$ 7. **Simplify:** $$5x = 8$$ 8. **Divide both sides by 5 to solve for $x$:** $$x = \frac{8}{5}$$ **Final answer:** $$x = \frac{8}{5}$$