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Chapter 6: Problem 130

If \(x\) represents a number, write an English sentence about the number that results in an equation with no solution.

Short Answer

Expert verified
The English sentence that results in an equation with no solution could be: 'A number is equal to that number plus one.' This translates to the equation \(x = x + 1\), which indeed, has no solution.

Step by step solution

01

Equation Construction

An example of an English sentence about a number that will result in an equation with no solution could be: 'A number is equal to that number plus one.' Let's break this sentence into the corresponding mathematical equation. Where it mentions a 'number', this will be represented by \(x\). The sentence 'A number is equal to that number plus one' translates to \(x = x + 1\).
02

Equation Analysis

The accuracy of this equation can be verified by trying to find a solution for \(x\). If done correctly, a contradiction or impossibility should appear proving that this equation indeed has no solution. If we subtract \(x\) from both sides of the equation in an attempt to isolate \(x\), we get \(0 = 1\), which is clearly a false statement. Therefore, the equation \(x = x + 1\) indeed has no valid solutions, making this equation a correct answer to the exercise.

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