First, we must evaluate the equation without the negative signs:
-1•-|f|=-16•-1
We are multiplying each side by -1 to cancel the negatives, but we will solve with them later. Remember, a negative number times a negative number equals a positive number.
|f|=16
Because absolute value measures the distance from 0 on a number line, there are two distances: a distance with a negative value and a distance with a positive value. So, if we must find a distance from 0, then a distance is -a and a.
|f|=16
f=-16 and 16
Now, let’s factor the negatives back into the equation
-|f|=-16
We know what f equals now, so we’ll input f=-16, 16 back into the equation:
-|-16|=-16
-(16)=-16
So, -16 is a solution. Now let’s check 16:
-|16|=-16
-(16)=-16
And, 16 is also a solution.
Answer: Therefore, the equation has two solutions.