Solving Absolute Value Equations Using Algebra

This week in math we learned how to solve an absolute value equation using algebra.

Our goal when solving an absolute value equation is to solve for X, the absolute value means X will always be positive.  We know an equation is absolute because it is determined with | signs surrounding the equation.

If our equation was:

We first isolate X to solve for it. Next we take the same equation but multiple it by -1 and solve for X, this is called piecewise notation.

Now that we have solved twice for one equation we take both answers for X and replace it in the equation wherever X is using the original equation (the one you didn’t use piecewise notation on).

After doing this it will determine whether both are solutions, only one, or none.  To keep in mind all answers are not going to be pretty so when solving if you get a fraction keep going with it because although it may not look like something your are used to it may end up turning out correct.