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AlgebraQ&A LibraryLet a and b be positive numbers such that a < b. State whether the absolute value equation has no solution, two negative solutions, two positive solutions, or one positive and one negative solution.|x − b| = -ano solutiontwo negative solutions two positive solutionsone positive and one negative solutionQuestion

Asked Sep 20, 2019

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Let *a* and *b* be positive numbers such that *a* < *b*. State whether the absolute value equation has no solution, two negative solutions, two positive solutions, or one positive and one negative solution.

|*x* − *b*| = -*a*

no solution

two negative solutions

two positive solutions

one positive and one negative solution

Step 1

To determine if the equation |*x* − *b*| = -*a *has no solution, two negative solutions, two positive solutions, one positive and one negative solution, provided that *a *and *b *are positive number such that *a < b.*

Step 2

Consider that *a *and *b *are positive number such that *a < b.*

Recall that the absolute difference of two number is a positive number.

So, the expression | x – b | is always a positive number for all values of *x*.

But *-a* is a negative number since *a *is a positive number.

Since the left-hand side of the equation |*x* ...

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