1. Stating the problem: Solve the inequality $$2 + 2x \geq 3x - 12$$ for $x$. 2. Write down the inequality: $$2 + 2x \geq 3x - 12$$ 3. To isolate $x$, subtract $2x$ from both sides: $$2 + \cancel{2x} \geq 3x - 12 - \cancel{2x}$$ which simplifies to $$2 \geq x - 12$$ 4. Next, add 12 to both sides to isolate $x$: $$2 + 12 \geq x - 12 + 12$$ which simplifies to $$14 \geq x$$ 5. This can be rewritten as $$x \leq 14$$ 6. Interpretation: The solution to the inequality is all values of $x$ less than or equal to 14. Final answer: $$x \leq 14$$