Exercise 55 Page 34

We are given the following absolute value equation. |x-4|=p In this equation, the number of solutions depends on the sign of p.

• If p is a negative number there are no solutions to this equation, as the absolute value of any number is always greater than or equal to 0.
• If p is 0, there will be one solution.
• If p is a positive number there will be two solutions, as x-4 can equal either p or - p.

Given all of the above information we can write a conclusion.