Without calculating, how do you know that the equation |4x-7|=-1 has no solution?
a. An absolute value cannot be positive.
b. An absolute value cannot be negative.
c. An absolute value equation must have one side equal to zero.
d. An absolute value cannot contain a negative constant inside it.
The correct answer is c. An absolute value equation must have one side equal to zero.
The absolute value of any expression is always non-negative, meaning it is either positive or zero. In the given equation, the right side is -1, which is negative. Since absolute values cannot be negative, it follows that there are no possible values for x that would satisfy the equation.