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. Complete the following two-column proof. Given: 3(x+1)=-x-9 Prove: x=-3

. Complete the following two-column proof. Given: 3(x+1)=-x-9 Prove: x=-3

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Two-Column Proof: Solving the Equation** **Given:** \(3(x + 1) = -x - 9\) **Prove:** \(x = -3\) | **Statement** | **Reason** | |---------------|------------| | 1. \(3(x + 1) = -x - 9\) | Given | | 2. \(3x + 3 = -x - 9\) | Distributive Property | | 3. \(4x + 3 = -9\) | Add \(x\) to both sides | | 4. \(4x = -12\) | Subtract 3 from both sides | | 5. \(x = -3\) | Divide both sides by 4 | This two-column proof demonstrates the step-by-step process of solving the given linear equation to prove that \(x = -3\). Each step involves a statement and the corresponding reason for the mathematical operation being performed.
Transcribed Image Text:**Two-Column Proof: Solving the Equation** **Given:** \(3(x + 1) = -x - 9\) **Prove:** \(x = -3\) | **Statement** | **Reason** | |---------------|------------| | 1. \(3(x + 1) = -x - 9\) | Given | | 2. \(3x + 3 = -x - 9\) | Distributive Property | | 3. \(4x + 3 = -9\) | Add \(x\) to both sides | | 4. \(4x = -12\) | Subtract 3 from both sides | | 5. \(x = -3\) | Divide both sides by 4 | This two-column proof demonstrates the step-by-step process of solving the given linear equation to prove that \(x = -3\). Each step involves a statement and the corresponding reason for the mathematical operation being performed.
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