1. **State the problem:** Solve the equation $$2(3x + 2) = 2x + 28$$ for $x$. 2. **Apply the distributive property:** $$2 \times 3x + 2 \times 2 = 2x + 28$$ $$6x + 4 = 2x + 28$$ 3. **Isolate variable terms on one side:** Subtract $2x$ from both sides: $$6x + 4 - \cancel{2x} = \cancel{2x} + 28 - 2x$$ $$6x - 2x + 4 = 28$$ $$4x + 4 = 28$$ 4. **Isolate the term with $x$:** Subtract 4 from both sides: $$4x + 4 - \cancel{4} = 28 - \cancel{4}$$ $$4x = 24$$ 5. **Solve for $x$ by dividing both sides by 4:** $$\frac{4x}{\cancel{4}} = \frac{24}{\cancel{4}}$$ $$x = 6$$ **Final answer:** $x = 6$