You have money in your wallet but you don't know the exact amount when a friend asks you you say that you have 100 dollars give or take 25. use an absolute value equation to find least and biggest amount of money in your pocket.

The least amount is 75 dollars.

The biggest amount is 125 dollars

Step-by-step explanation:

The absolute value function will help us determine a  range of possible values since we do not know the exact amount of money.

Defining the function.

Let x be the exact amount of money in my pocket, we can define the equation

And we know that the difference between the exact amount of money with 100 dollars must be either 25 dollars more than what we estimated, or 25 dollars less than the estimation.  So we can write:

We have a difference inside an absolute value, since we know the difference must be either +25 or -25.

Solving for x

Using the definition of absolute value we have

So if the inside of the absolute value is positive we have the first line of the piece-wise function, that is

Solving for x give us

If the inside of the absolute value is negative we have to use the second line of the piece-wise function definition

Solving for x give us

So the least amount of money in my pocket is 75 dollars and the biggest amount is 125 dollars.