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High School Math Geometry Glencoe Geometry

The statement for the indirect proof.

The statement for the indirect proof.

Glencoe Geometry

Glencoe Geometry

14th Edition

ISBN: 9780076639304

Author: Cuevas, day Carter

Publisher: Not Avail

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Chapter 5.4, Problem 6CYU

To determine

The statement for the indirect proof.

Expert Solution & Answer

Explanation of Solution

Given information:

If 3x−4>8, then x>4 .

Calculation:

In an indirect proof or proof by contradiction, assume that the conclusion is false. By showing the assumption to be logically impossible, prove the assumption is false and the original conclusion is true.

Following steps are used for the indirect proof are as shown below:

Firstly, the negation of x>4 is x≤4 . So, assume that x<4 or x=4 is true.

Secondly, make a table with several possibilities for x assuming x<4 or x=4 is true:

Glencoe Geometry, Chapter 5.4, Problem 6CYU

When x<4,3x−4<8 and when x=4,3x−4=8 .

In both the steps, the assumption leads to the contradiction of the given information that 3x−4>8. therefore, the assumption that x≤4 must be false, so the original conclusion that x>4 must be true.

Chapter 5.4, Problem 5CYU

Chapter 5.4, Problem 7CYU

Chapter 5 Solutions

Glencoe Geometry

Ch. 5.1 - Prob. 1ACYP Ch. 5.1 - Prob. 1BCYP Ch. 5.1 - Prob. 1CCYP Ch. 5.1 - Prob. 2CYP Ch. 5.1 - Prob. 3ACYP Ch. 5.1 - Prob. 3BCYP Ch. 5.1 - Prob. 3CCYP Ch. 5.1 - Prob. 4ACYP Ch. 5.1 - Prob. 4BCYP Ch. 5.1 - Prob. 1CYU

Ch. 5.1 - Prob. 2CYU Ch. 5.1 - Prob. 3CYU Ch. 5.1 - Prob. 4CYU Ch. 5.1 - Prob. 5CYU Ch. 5.1 - Prob. 6CYU Ch. 5.1 - Prob. 7CYU Ch. 5.1 - Prob. 8CYU Ch. 5.1 - Prob. 9PPS Ch. 5.1 - Prob. 10PPS Ch. 5.1 - Prob. 11PPS Ch. 5.1 - Prob. 12PPS Ch. 5.1 - Prob. 13PPS Ch. 5.1 - Prob. 14PPS Ch. 5.1 - Prob. 15PPS Ch. 5.1 - Prob. 16PPS Ch. 5.1 - Prob. 17PPS Ch. 5.1 - Prob. 18PPS Ch. 5.1 - Prob. 19PPS Ch. 5.1 - Prob. 20PPS Ch. 5.1 - Prob. 21PPS Ch. 5.1 - Prob. 22PPS Ch. 5.1 - Prob. 23PPS Ch. 5.1 - Prob. 24PPS Ch. 5.1 - Prob. 25PPS Ch. 5.1 - Prob. 26PPS Ch. 5.1 - Prob. 27PPS Ch. 5.1 - Prob. 28PPS Ch. 5.1 - Prob. 29PPS Ch. 5.1 - Prob. 30PPS Ch. 5.1 - Prob. 31PPS Ch. 5.1 - Prob. 32PPS Ch. 5.1 - Prob. 33PPS Ch. 5.1 - Prob. 34PPS Ch. 5.1 - Prob. 35PPS Ch. 5.1 - Prob. 36PPS Ch. 5.1 - Prob. 37PPS Ch. 5.1 - Prob. 38PPS Ch. 5.1 - Prob. 39PPS Ch. 5.1 - Prob. 40PPS Ch. 5.1 - Prob. 41PPS Ch. 5.1 - Prob. 42PPS Ch. 5.1 - Prob. 43PPS Ch. 5.1 - Prob. 44PPS Ch. 5.1 - Prob. 45PPS Ch. 5.1 - Prob. 46PPS Ch. 5.1 - Prob. 47PPS Ch. 5.1 - 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Prob. 60SPR Ch. 5.5 - Prob. 61SR Ch. 5.5 - Prob. 62SR Ch. 5.5 - Prob. 63SR Ch. 5.6 - Prob. 1ACYP Ch. 5.6 - Prob. 1BCYP Ch. 5.6 - Prob. 2ACYP Ch. 5.6 - Prob. 2BCYP Ch. 5.6 - Prob. 3CYP Ch. 5.6 - Prob. 4CYP Ch. 5.6 - Prob. 5CYP Ch. 5.6 - Prob. 1CYU Ch. 5.6 - Prob. 2CYU Ch. 5.6 - Prob. 3CYU Ch. 5.6 - Prob. 4CYU Ch. 5.6 - Prob. 5CYU Ch. 5.6 - Prob. 6CYU Ch. 5.6 - Prob. 7CYU Ch. 5.6 - Prob. 8CYU Ch. 5.6 - Prob. 9CYU Ch. 5.6 - Prob. 10PPS Ch. 5.6 - Prob. 11PPS Ch. 5.6 - Prob. 12PPS Ch. 5.6 - Prob. 13PPS Ch. 5.6 - Prob. 14PPS Ch. 5.6 - Prob. 15PPS Ch. 5.6 - Prob. 16PPS Ch. 5.6 - Prob. 17PPS Ch. 5.6 - Prob. 18PPS Ch. 5.6 - Prob. 19PPS Ch. 5.6 - Prob. 20PPS Ch. 5.6 - Prob. 21PPS Ch. 5.6 - Prob. 22PPS Ch. 5.6 - Prob. 23PPS Ch. 5.6 - Prob. 24PPS Ch. 5.6 - Prob. 25PPS Ch. 5.6 - Prob. 26PPS Ch. 5.6 - Prob. 27PPS Ch. 5.6 - Prob. 28PPS Ch. 5.6 - Prob. 29PPS Ch. 5.6 - Prob. 30PPS Ch. 5.6 - Prob. 31PPS Ch. 5.6 - Prob. 32PPS Ch. 5.6 - Prob. 33PPS Ch. 5.6 - Prob. 34PPS Ch. 5.6 - Prob. 35PPS Ch. 5.6 - Prob. 36PPS Ch. 5.6 - Prob. 37PPS Ch. 5.6 - Prob. 38HP Ch. 5.6 - Prob. 39HP Ch. 5.6 - Prob. 40HP Ch. 5.6 - Prob. 41HP Ch. 5.6 - Prob. 42HP Ch. 5.6 - Prob. 43STP Ch. 5.6 - Prob. 44STP Ch. 5.6 - Prob. 45STP Ch. 5.6 - Prob. 46STP Ch. 5.6 - Prob. 47SPR Ch. 5.6 - Prob. 48SPR Ch. 5.6 - Prob. 49SPR Ch. 5.6 - Prob. 50SPR Ch. 5.6 - Prob. 51SPR Ch. 5.6 - Prob. 52SPR Ch. 5.6 - Prob. 53SPR Ch. 5.6 - Prob. 54SPR Ch. 5.6 - Prob. 55SPR Ch. 5.6 - Prob. 56SR Ch. 5.6 - Prob. 57SR Ch. 5.6 - Prob. 58SR Ch. 5 - Prob. 1GRFC Ch. 5 - Prob. 2GRFC Ch. 5 - Prob. 3GRFC Ch. 5 - Prob. 4GRFC Ch. 5 - Prob. 5GRFC Ch. 5 - Prob. 6GRFC Ch. 5 - Prob. 7GRFC Ch. 5 - Prob. 8GRFC Ch. 5 - Prob. 9GRFC Ch. 5 - Prob. 10GRFC Ch. 5 - Prob. 11GRFC Ch. 5 - Prob. 12GRFC Ch. 5 - Prob. 1MCQ Ch. 5 - Prob. 2MCQ Ch. 5 - Prob. 3MCQ Ch. 5 - Prob. 4MCQ Ch. 5 - Prob. 5MCQ Ch. 5 - Prob. 6MCQ Ch. 5 - Prob. 7MCQ Ch. 5 - Prob. 8MCQ Ch. 5 - Prob. 9MCQ Ch. 5 - Prob. 10MCQ Ch. 5 - Prob. 11MCQ Ch. 5 - Prob. 12MCQ Ch. 5 - Prob. 13MCQ Ch. 5 - Prob. 14MCQ Ch. 5 - Prob. 15MCQ Ch. 5 - 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