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The problem asks us to provide a two-column proof to show that if $25 = -7(y - 3) + 5y$, then $-2 = y$.

AlgebraLinear EquationsEquation SolvingProofProperties of Equality
2025/4/6

1. Problem Description

The problem asks us to provide a two-column proof to show that if 25=−7(y−3)+5y25 = -7(y - 3) + 5y, then −2=y-2 = y.

2. Solution Steps

We will solve the equation 25=−7(y−3)+5y25 = -7(y - 3) + 5y step by step, justifying each step with a property or definition.
Statement | Reason
------- | --------

1. $25 = -7(y - 3) + 5y$ |

1. Given

2. $25 = -7y + 21 + 5y$ |

2. Distributive Property

3. $25 = -2y + 21$ |

3. Combine Like Terms

4. $25 - 21 = -2y + 21 - 21$ |

4. Subtraction Property of Equality

5. $4 = -2y$ |

5. Simplify

6. $\frac{4}{-2} = \frac{-2y}{-2}$ |

6. Division Property of Equality

7. $-2 = y$ |

7. Simplify

3. Final Answer

Therefore, the two-column proof is as follows:
Statement | Reason
------- | --------

1. $25 = -7(y - 3) + 5y$ |

1. Given

2. $25 = -7y + 21 + 5y$ |

2. Distributive Property

3. $25 = -2y + 21$ |

3. Combine Like Terms

4. $25 - 21 = -2y + 21 - 21$ |

4. Subtraction Property of Equality

5. $4 = -2y$ |

5. Simplify

6. $\frac{4}{-2} = \frac{-2y}{-2}$ |

6. Division Property of Equality

7. $-2 = y$ |

7. Simplify

Final Answer: −2=y-2 = y

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