1. **State the problem:** Solve the equation $$2.5(x + 4) + x = 38$$ for $x$. 2. **Apply the distributive property:** Multiply $2.5$ by both $x$ and $4$: $$2.5x + 2.5 \times 4 + x = 38$$ $$2.5x + 10 + x = 38$$ 3. **Combine like terms:** Add $2.5x$ and $x$: $$2.5x + x = 3.5x$$ So the equation becomes: $$3.5x + 10 = 38$$ 4. **Isolate the variable term:** Subtract $10$ from both sides: $$3.5x + \cancel{10} - \cancel{10} = 38 - 10$$ $$3.5x = 28$$ 5. **Solve for $x$:** Divide both sides by $3.5$: $$\frac{3.5x}{\cancel{3.5}} = \frac{28}{\cancel{3.5}}$$ $$x = 8$$ **Final answer:** $$x = 8$$