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High School Math Calculus EBK PRECALCULUS W/LIMITS

Determine whether the given statement is true or false.

Determine whether the given statement is true or false.

EBK PRECALCULUS W/LIMITS

EBK PRECALCULUS W/LIMITS

3rd Edition

ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter A.5, Problem 99E

To determine

Determine whether the given statement is true or false.

Expert Solution & Answer

Answer to Problem 99E

The statement " $x+10−x−10=0$ has no solution" is true

Explanation of Solution

Given:

The equation:

$x+10−x−10=0$

Consider the following equation:

$x+10−x−10=0$

Check that the above equation has solution or not.

Isolate the radical first.

Add $x−10$ to both sides of the equation $x+10−x−10=0$

$x+10−x−10+x−10=0+x−10$

Combine like terms to simplify the expression:

$x+10=x−10$

Further raise both sides to the power of the index which is 2.

Raise power 2 to both sides:

$(x+10)2=(x−10)2$

Simplify the expression:

$x+10=x−10$

Subtract $x$ from both sides:

$x+ 10–x=x–10–x$

Combine like terms:

$10=–10$

Because $10=–10$ is a false statement,

Therefore, the equation has no solution.

Hence the statement " $x+10−x−10=0$ has no solution" is true.

Chapter A.5, Problem 98E

Chapter A.5, Problem 100E

Chapter A Solutions

EBK PRECALCULUS W/LIMITS

Ch. A.1 - Prob. 1E Ch. A.1 - Prob. 2E Ch. A.1 - Prob. 3E Ch. A.1 - Prob. 4E Ch. A.1 - Prob. 5E Ch. A.1 - Prob. 6E Ch. A.1 - Prob. 7E Ch. A.1 - Prob. 8E Ch. A.1 - Prob. 9E Ch. A.1 - Prob. 10E

Ch. A.1 - Prob. 11E Ch. A.1 - Prob. 12E Ch. A.1 - Prob. 13E Ch. A.1 - Prob. 14E Ch. A.1 - Prob. 15E Ch. A.1 - Prob. 16E Ch. A.1 - Prob. 17E Ch. A.1 - Prob. 18E Ch. A.1 - Prob. 19E Ch. A.1 - Prob. 20E Ch. A.1 - Prob. 21E Ch. A.1 - Prob. 22E Ch. A.1 - Prob. 23E Ch. A.1 - Prob. 24E Ch. A.1 - Prob. 25E Ch. A.1 - Prob. 26E Ch. A.1 - Prob. 27E Ch. A.1 - Prob. 28E Ch. A.1 - Prob. 29E Ch. A.1 - Prob. 30E Ch. A.1 - Prob. 31E Ch. A.1 - Prob. 32E Ch. A.1 - Prob. 33E Ch. A.1 - Prob. 34E Ch. A.1 - Prob. 35E Ch. A.1 - Prob. 36E Ch. A.1 - Prob. 37E Ch. A.1 - Prob. 38E Ch. A.1 - Prob. 39E Ch. A.1 - Prob. 40E Ch. A.1 - Prob. 41E Ch. A.1 - Prob. 42E Ch. A.1 - Prob. 43E Ch. A.1 - Prob. 44E Ch. A.1 - Prob. 45E Ch. A.1 - Prob. 46E Ch. A.1 - Prob. 47E Ch. A.1 - Prob. 48E Ch. A.1 - Prob. 49E Ch. A.1 - Prob. 50E Ch. A.1 - Prob. 51E Ch. A.1 - Prob. 52E Ch. A.1 - Prob. 53E Ch. A.1 - Prob. 54E Ch. A.1 - Prob. 55E Ch. A.1 - Prob. 56E Ch. A.1 - Prob. 57E Ch. A.1 - Prob. 58E Ch. A.1 - Prob. 59E Ch. 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