Whether the statement “ x < − 3 or x > 1 may also be written as 1 < x < − 3 ” is true or false and explain the reason if the given statement is false.

Question

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Answer 1

Question

Chapter 17, Problem 1RE

To determine

Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is false_.

Explanation of Solution

Consider the inequality 1<x<−3.

The given inequality 1<x<−3 can be written as 1<x and x<−3 which is inconsistent.

Note that, if 1<x then x<−3 and if x<−3 then x<1, so the inequality 1<x<−3 is inconsistent.

Therefore, the given statement is false_.

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Answer 2

Question

Chapter 17, Problem 1RE

To determine

Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is false_.

Explanation of Solution

Consider the inequality 1<x<−3.

The given inequality 1<x<−3 can be written as 1<x and x<−3 which is inconsistent.

Note that, if 1<x then x<−3 and if x<−3 then x<1, so the inequality 1<x<−3 is inconsistent.

Therefore, the given statement is false_.

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Answer 3

Question

Chapter 17, Problem 1RE

To determine

Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is false_.

Explanation of Solution

Consider the inequality 1<x<−3.

The given inequality 1<x<−3 can be written as 1<x and x<−3 which is inconsistent.

Note that, if 1<x then x<−3 and if x<−3 then x<1, so the inequality 1<x<−3 is inconsistent.

Therefore, the given statement is false_.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 17, Problem 1RE

To determine

Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is false_.

Explanation of Solution

Consider the inequality 1<x<−3.

The given inequality 1<x<−3 can be written as 1<x and x<−3 which is inconsistent.

Note that, if 1<x then x<−3 and if x<−3 then x<1, so the inequality 1<x<−3 is inconsistent.

Therefore, the given statement is false_.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 17, Problem 1RE

To determine

Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is false_.

Explanation of Solution

Consider the inequality 1<x<−3.

The given inequality 1<x<−3 can be written as 1<x and x<−3 which is inconsistent.

Note that, if 1<x then x<−3 and if x<−3 then x<1, so the inequality 1<x<−3 is inconsistent.

Therefore, the given statement is false_.

Answer 6

Chapter 17, Problem 1RE

To determine

Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Expert Solution & Answer

Answer to Problem 1RE

The given statement is false_.

Explanation of Solution

Consider the inequality 1<x<−3.

The given inequality 1<x<−3 can be written as 1<x and x<−3 which is inconsistent.

Note that, if 1<x then x<−3 and if x<−3 then x<1, so the inequality 1<x<−3 is inconsistent.

Therefore, the given statement is false_.

Answer 7

Chapter 17, Problem 1RE

To determine

Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Answer 8

Expert Solution & Answer

Answer to Problem 1RE

The given statement is false_.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Consider the inequality 1<x<−3.

The given inequality 1<x<−3 can be written as 1<x and x<−3 which is inconsistent.

Note that, if 1<x then x<−3 and if x<−3 then x<1, so the inequality 1<x<−3 is inconsistent.

Therefore, the given statement is false_.

Answer 12

Ch. 17.1 - For −6 < 3, determine the inequality if 1. 8 is...Ch. 17.1 - Prob. 2PE Ch. 17.1 - For the inequality −6 < 3, state the inequality...Ch. 17.1 - Prob. 4PE Ch. 17.1 - Prob. 5PE Ch. 17.1 - In Exercises 1–4, make the given changes in the...Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - In Exercises 5–12, for the inequality 4 < 9, state...

Whether the statement “ x < − 3 or x > 1 may also be written as 1 < x < − 3 ” is true or false and explain the reason if the given statement is false.

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Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Answer to Problem 1RE

Explanation of Solution

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Chapter 17 Solutions

Whether the statement “ x &lt; − 3 or x &gt; 1 may also be written as 1 &lt; x &lt; − 3 ” is true or false and explain the reason if the given statement is false.

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Whether the statement “x<−3 or x>1 may also be written as 1<x<−3” is true or false and explain the reason if the given statement is false.

Answer to Problem 1RE

Explanation of Solution

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Chapter 17 Solutions

Whether the statement “ x < − 3 or x > 1 may also be written as 1 < x < − 3 ” is true or false and explain the reason if the given statement is false.