# 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

2021-02-01
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.

### Relevant Questions

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
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
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
Let a, b and c be a real numbers such that a>0, b<0 and c<0. Find the sign of each expression.
a) -b
b) a+c
c) c-a
d) $$ab^2$$
Let a, b and c be a real numbers such that a>0, b<0 and c<0. Find the sign of each expression.
a) -b
b) a+c
c) c-a
d) $$\displaystyle{a}{b}^{{2}}$$
Let a, b and c be a real numbers such that a>0, b<0 and c<0. Find the sign of each expression.
a) -a
b) bc
c) a-b
d) ab+ac