This gives practice for computing the absolute value.

How You Can (And Should) Get More Practice!

Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for you.

Theoretically Easier Difficulty Problem

Start by moving everything to one side of the equation.
Once you have everything on one side, rewrite it in piece-wise form to get rid of the absolute values.
Set each subfunction of the piece-wise expression equal to zero and solve. Then check that the solution you find is in the domain of that subfunction.
Don’t forget that the answer is the sum of the valid solutions.
Solve the equality for . If there are no solutions, enter DNE

The sum of valid -solutions is:

Theoretically Medium Difficulty Problem

Start by moving everything to one side of the equation.
Once you have everything on one side, rewrite it in piece-wise form to get rid of the absolute values.
Set each subfunction of the piece-wise expression equal to zero and solve. Then check that the solution you find is in the domain of that subfunction.
Don’t forget that the answer is the sum of the valid solutions.
Solve the equality for . If there are no solutions, enter DNE [Note this problem can generate problems where answers exist, and where they don’t exist, so try hitting the “Another” button in the top right of the page until you have done examples of both!]

The sum of valid -solutions is:

Theoretically Harder Difficulty Problem

Start by moving everything to one side of the equation.
Once you have everything on one side, rewrite it in piece-wise form to get rid of the absolute values. Remember for quadratics this requires you to use a sign chart to determine which domain(s) have positive values inside the absolute value, versus negative values.
Set each subfunction of the piece-wise expression equal to zero and solve. Then check that the solution you find is in the domain of that subfunction.
Don’t forget that the answer is the sum of the valid solutions.
Solve the equality for . If there are no solutions, enter DNE [Note this problem can generate problems where answers exist, and where they don’t exist, so try hitting the “Another” button in the top right of the page until you have done examples of both!]

The sum of valid -solutions is: