How do you graph and solve # |x-4|<9#?

1 Answer

Answer:

#-5 < x < 13#

Explanation:

When working with absolute value inequalities, we need to remember that the absolute value function will return a positive value regardless of what lies within. For instance, if we have

#x=3#, #x# can be 3 or it can be #-3#. And so in our question we need to address this:

#abs(x-4)<9=>x-4 < pm9=> -9 < x-4 < 9#

We can now solve this by adding 4 to all sides:

#-9 < x-4 < 9#

#-9 color(red)(+4)< x-4color(red)(+4) < 9color(red)(+4)#

#-5 < x < 13#

We can graph this on a number line by placing hollow circles around #-5# and 13 (to indicate that all the points up to but not including #-5# and 13 are part of the solution) and then drawing a line connecting the two.

Tony B