Let a and b be positive numbers such that a&lt;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

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Let a and b be positive numbers such that a&amp;lt;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

saiyansruleA · Accepted Answer

Consider that a and b are positive number such that a&amp;lt;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−b|=−a is a positive number and right-hand side of the equation |x−b|=−a is a negative number hence the equation |x−b|=−a has no solution.

Let a and b be positive numbers such that a < b. State whether the absolute value equation

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