Solving absolute value equations?

|x+1| = |x-4|

x + 1 = -x + 4

2x = 3

x = 3/2

or:

-x - 1 = x - 4

2x = 3

x = 3/2

same as above

|x-3| = 5 + |x+1|

|x - 3| - |x + 1| = 5

x - 3 - x - 1 = -5

-4 ≠ -5

hence there are no solutions.

To solve the first one...

Ix+1I = Ix-4I

x+1 = x-4 or x+1 = -x+4 The trick is in the line. As absolute value is the distance from zero making the whole thing negative just puts the point on the opposite side of the origin.

Solving...

x+5 = x or 2x = 3

Cannot solve or x =1.5

Also you can graph them. This website is useful http://www.umsl.edu/~defreeseca/intalg/ch2extra/ab...

You can solve absolute value equation by taking x > = 0 and then x < 0.Put all the values of x in the equation and check which is correct and follows the equation

Me, Bill gates and Chuck norris said this is the best:

www.khanacademy.org

Good Luck!!!!