1. State the problem: Which of the expressions below is equal to $10x + 30$? A) $10(x + 3)$ B) $9x + 24 + x + 6$ C) $16x + 40 - 8x - 20$ D) $5(x + 6)$. 2. Formula and important rules: Use the distributive property and combining like terms to simplify expressions. $$a(b+c)=ab+ac$$ Distribute multiplication over addition, combine like terms (terms with the same variable), and factor when useful. 3. Check option A: Start with $10(x+3)$. $$10(x+3)=10x+30$$ Therefore A equals $10x+30$. 4. Check option B: Start with $9x+24+x+6$. $$9x+24+x+6=(9x+x)+(24+6)=10x+30$$ Therefore B equals $10x+30$. 5. Check option C: Start with $16x+40-8x-20$. $$16x+40-8x-20=(16x-8x)+(40-20)=8x+20$$ Therefore C simplifies to $8x+20$, which is not $10x+30$. 6. Check option D: Start with $5(x+6)$. $$5(x+6)=5x+30$$ Therefore D equals $5x+30$, which is not $10x+30$. 7. Final answer: Options A and B are equal to $10x+30$.