Solve following.

                                 |2x - 5 |= 9

Solution

Now, recall that absolute value does not just make all minus signs in plus signs. In order to solve these we've got to employ the formula above as in all cases the number on the right side of the equal sign is positive.

There actually isn't much to do here other than using the formula from above as noted above.  All we have to note is that in the formula above p represents whatever is on the inside of the absolute value bars and so in this case we have,

                                                           2 x - 5 = -9          or    2 x - 5 = 9

At this instance we've got two linear equations which are easy to solve.

2 x = -4           or         2 x = 14

x = -2  or       x = 7

Thus, we've got two solutions to the equation

                      x = -2 and    x =7 .

Now, let's take a look at how to deal with equations for which b is zero or negative.  We'll do this with an example.