Absolute value

by **san** Thu Jan 01, 2009 10:28 pm

Hi Stacey / Ron,

|x^2 + 16| - 5 = 27

What is correct method to solve the equation

|x^2 + 16 | = 33

x^2 + 16 = 33
x^2 = 17
x = + - root of 17

or

x^2 + 16 = -33
x^2 = -49

x = undefined in gmat.

AM I correct ?

or below method is right.

|x2 + 16| - 5 = 27

|x2 + 16| can be written x2 +16. Using this information, we can solve for x:

x2 + 16 - 5 = 27
x2 + 11 = 27
x2 = 16
x = 4 or x = -4

Since |-4| = |4| = 4, we know that |x| = 4

by **JonathanSchneider** Fri Jan 02, 2009 11:37 am

You've made a slight mistake up top that has thrown off your math. You should have arrived at 4 or -4 there as well. It's just a simple addition error: 27 + 5 = 32. When you come out with something like x^2 - 16 = 33, beware: that 16 would go better with a 32, so you may have made a small mistake.

Also, either of your versions (top or bottom) will work just fine. Notice that what you have done below is to simply eliminate the second case (when what's inside the absolute value is negative) because x^2 + 16 cannot be negative.