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

Question
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

Answers (1)

2021-01-11
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 − 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.
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