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Statement Reason 1. -5(1 – 5x) + 5(-8x– 2) = -4x 1. Given -8x 2. -5 + 25x – 40x – 10 = -4x – 2. A 8x 3. 3. Combine like terms 4. -15 = 3x 4. C 5. x= -5 5. Division Property of Equality

Statement Reason 1. -5(1 – 5x) + 5(-8x– 2) = -4x 1. Given -8x 2. -5 + 25x – 40x – 10 = -4x – 2. A 8x 3. 3. Combine like terms 4. -15 = 3x 4. C 5. x= -5 5. Division Property of Equality

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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- **Equation**: \(-15x - 15 = -12x\) - **Options**: 1. Addition Property of Equality 2. Subtraction Property of Equality 3. Distributive Property This question appears to test the understanding of algebraic properties. The focus is on identifying which property justifies the given equation transformation.
Transcribed Image Text:- **Equation**: \(-15x - 15 = -12x\) - **Options**: 1. Addition Property of Equality 2. Subtraction Property of Equality 3. Distributive Property This question appears to test the understanding of algebraic properties. The focus is on identifying which property justifies the given equation transformation.
**Two-Column Proof Explanation** **Problem:** When given \(-5(1 - 5x) + 5(-8x - 2) = -4x - 8x\) and trying to prove that \(x = -5\), what should be placed in line C of the two-column proof? **Two-Column Proof:** | Statement | Reason | |------------------------------------------|------------------------------------| | 1. \(-5(1 - 5x) + 5(-8x - 2) = -4x - 8x\) | 1. Given | | 2. \(-5 + 25x - 40x - 10 = -4x - 8x\) | 2. Distribute | | 3. \(-15 - 15x = -12x\) | 3. Combine like terms | | 4. \(-15 = 3x\) | 4. Simplify (Subtract \(15x\) from both sides) | | 5. \(x = -5\) | 5. Division Property of Equality | **Explanation:** 1. **Given:** Start with the initial equation. 2. **Distribute:** Expand both terms on the left side by distributing the coefficients through the parentheses. 3. **Combine like terms:** Group and simplify similar terms on both sides. 4. **Simplify:** Move terms to isolate the variable term on one side of the equation. 5. **Division Property of Equality:** Solve for \(x\) by dividing both sides by the coefficient of the variable. **Missing Statements and Reasons:** - For statement 3, you need to combine like terms on both sides of the equation, simplifying to \(-15 - 15x = -12x\). - In statement 4, isolate the variable \(x\) after simplifying the equation, leading to \(-15 = 3x\). - Statement 5 solves for \(x\) by applying the Division Property of Equality, resulting in \(x = -5\).
Transcribed Image Text:**Two-Column Proof Explanation** **Problem:** When given \(-5(1 - 5x) + 5(-8x - 2) = -4x - 8x\) and trying to prove that \(x = -5\), what should be placed in line C of the two-column proof? **Two-Column Proof:** | Statement | Reason | |------------------------------------------|------------------------------------| | 1. \(-5(1 - 5x) + 5(-8x - 2) = -4x - 8x\) | 1. Given | | 2. \(-5 + 25x - 40x - 10 = -4x - 8x\) | 2. Distribute | | 3. \(-15 - 15x = -12x\) | 3. Combine like terms | | 4. \(-15 = 3x\) | 4. Simplify (Subtract \(15x\) from both sides) | | 5. \(x = -5\) | 5. Division Property of Equality | **Explanation:** 1. **Given:** Start with the initial equation. 2. **Distribute:** Expand both terms on the left side by distributing the coefficients through the parentheses. 3. **Combine like terms:** Group and simplify similar terms on both sides. 4. **Simplify:** Move terms to isolate the variable term on one side of the equation. 5. **Division Property of Equality:** Solve for \(x\) by dividing both sides by the coefficient of the variable. **Missing Statements and Reasons:** - For statement 3, you need to combine like terms on both sides of the equation, simplifying to \(-15 - 15x = -12x\). - In statement 4, isolate the variable \(x\) after simplifying the equation, leading to \(-15 = 3x\). - Statement 5 solves for \(x\) by applying the Division Property of Equality, resulting in \(x = -5\).
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