# 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| = -ano solutiontwo negative solutions    two positive solutionsone positive and one negative solution

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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.

|xb| = -a
no solution
two negative solutions
two positive solutions
one positive and one negative solution

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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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