1. **Determine if the two equations are equivalent:** **Problem 1:** Given equations: $x - 7 = -25$ and $x = -18$ Step 1: Solve the first equation for $x$. $$x - 7 = -25$$ Add 7 to both sides: $$x - 7 + 7 = -25 + 7$$ $$x = -18$$ Step 2: Compare with the second equation $x = -18$. They are the same, so the equations are equivalent. **Problem 2:** Given equations: $x + 14 = 25$ and $x = -11$ Step 1: Solve the first equation for $x$. $$x + 14 = 25$$ Subtract 14 from both sides: $$x + 14 - 14 = 25 - 14$$ $$x = 11$$ Step 2: Compare with the second equation $x = -11$. They are not the same, so the equations are not equivalent. **Problem 3:** Given equations: $x - 4 = -18$ and $x = -14$ Step 1: Solve the first equation for $x$. $$x - 4 = -18$$ Add 4 to both sides: $$x - 4 + 4 = -18 + 4$$ $$x = -14$$ Step 2: Compare with the second equation $x = -14$. They are the same, so the equations are equivalent. 2. **Use the distributive property to write an equivalent expression:** **Problem 1:** $$5(x - y + 1) = 5 \cdot x - 5 \cdot y + 5 \cdot 1 = 5x - 5y + 5$$ **Problem 2:** $$-1(9 - 3m) = -1 \cdot 9 - (-1) \cdot 3m = -9 + 3m$$ **Problem 3:** $$(x - y)6 = x \cdot 6 - y \cdot 6 = 6x - 6y$$ 3. **Combine like terms to write an equivalent expression:** **Problem 1:** $$5y - 10y = (5 - 10)y = -5y$$ **Problem 2:** $$3 + 4x - 4y + 12x + 3y = 3 + (4x + 12x) + (-4y + 3y) = 3 + 16x - y$$ **Problem 3:** $$34x - 34y + 34x - 1 = (34x + 34x) - 34y - 1 = 68x - 34y - 1$$