1. **State the problem:** Solve the equation $2x + 3x = 15$ by collecting like terms and isolating the variable. 2. **Formula and rules:** When adding terms with the same variable, add their coefficients: $ax + bx = (a+b)x$. 3. **Combine like terms:** $$2x + 3x = (2+3)x = 5x$$ 4. **Rewrite the equation:** $$5x = 15$$ 5. **Isolate $x$ by dividing both sides by 5:** $$x = \frac{15}{5}$$ 6. **Show cancellation:** $$x = \frac{\cancel{15}}{\cancel{5}} = 3$$ 7. **Final answer:** $$x = 3$$ This method applies to all similar equations: combine like terms, then isolate the variable by dividing both sides by the coefficient.