1. **State the problem:** Solve the inequality $$3 - 2x \leq x + 15$$. 2. **Isolate the variable terms:** Move all terms involving $x$ to one side and constants to the other. $$3 - 2x \leq x + 15$$ Subtract $x$ from both sides: $$3 - 2x - x \leq 15$$ This simplifies to: $$3 - 3x \leq 15$$ 3. **Isolate the $x$ term:** Subtract 3 from both sides: $$3 - 3x - 3 \leq 15 - 3$$ $$-3x \leq 12$$ 4. **Divide both sides by $-3$:** Remember, dividing by a negative number reverses the inequality sign. $$\cancel{-3}x \geq \frac{12}{\cancel{-3}}$$ $$x \geq -4$$ 5. **Final answer:** The solution to the inequality is $$x \geq -4$$. This means all values of $x$ greater than or equal to $-4$ satisfy the inequality.