Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
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Exercise 15 Page 47

Can an absolute value produce a negative result?

A negative value can never be the result of an absolute value.

Practice makes perfect
The left-hand side of the equation is an absolute value and, therefore, its result will always be non-negative. The right-hand side is a single term with x and a coefficient of positive 6.


If we substitute x=- 2 into the equation, the right-hand side will equal a negative number, the product of a positive and a negative number is always negative. This means we have a contradiction, an absolute value cannot equal a negative number. Therefore, the solution must be extraneous.