Equivalent Expressions D978F8

1. **State the problem:** We need to find which expressions are equivalent to $$2(7m + 7) + 9$$. 2. **Start by simplifying the original expression:** $$2(7m + 7) + 9 = 2 \times 7m + 2 \times 7 + 9 = 14m + 14 + 9$$ 3. **Combine like terms:** $$14m + 14 + 9 = 14m + 23$$ 4. **Check each given expression for equivalence:** - Expression 1: $$2(7 + 7m) + 9$$ Rewrite inside parentheses: $$7 + 7m = 7m + 7$$ (commutative property) So this is the same as the original expression, which simplifies to $$14m + 23$$. - Expression 2: $$23m + 14$$ This is $$23m + 14$$, which is not equal to $$14m + 23$$. - Expression 3: $$2(6m + m + 7) + 9$$ Simplify inside parentheses: $$6m + m = 7m$$, so it becomes $$2(7m + 7) + 9$$, which is the original expression. - Expression 4: $$(7m + 7)2 + 9$$ Rewrite as $$2(7m + 7) + 9$$, which is the original expression. 5. **Conclusion:** Expressions 1, 3, and 4 are equivalent to the original expression $$2(7m + 7) + 9$$. **Final answer:** The equivalent expressions are: - $$2(7 + 7m) + 9$$ - $$2(6m + m + 7) + 9$$ - $$(7m + 7)2 + 9$$