1. **State the problem:** Show that the expressions $-0.75(-4f + 12)$ and $(5f + 9) - (2f + 18)$ are equivalent. 2. **Rewrite the expressions:** - First expression: $-0.75(-4f + 12)$ - Second expression: $(5f + 9) - (2f + 18)$ 3. **Simplify the first expression:** Use the distributive property: $a(b + c) = ab + ac$ $$-0.75(-4f + 12) = -0.75 \times -4f + (-0.75) \times 12$$ Calculate each term: $$-0.75 \times -4f = 3f$$ $$-0.75 \times 12 = -9$$ So, $$-0.75(-4f + 12) = 3f - 9$$ 4. **Simplify the second expression:** Apply subtraction to each term inside the parentheses: $$(5f + 9) - (2f + 18) = 5f + 9 - 2f - 18$$ Combine like terms: $$5f - 2f = 3f$$ $$9 - 18 = -9$$ So, $$(5f + 9) - (2f + 18) = 3f - 9$$ 5. **Compare the simplified expressions:** Both simplify to: $$3f - 9$$ Therefore, the expressions $-0.75(-4f + 12)$ and $(5f + 9) - (2f + 18)$ are equivalent. **Final answer:** $$-0.75(-4f + 12) = (5f + 9) - (2f + 18) = 3f - 9$$