How do you graph and solve # | x - 2 | > 1#?

1 Answer
May 19, 2017

Answer:

#x<1 " and " x > 3#

Explanation:

Absolute value functions need to be broken into two functions:
#(x-2) > 1 " and " -(x-2) > 1#

Solve for #x#:

#x -2 + 2 > 1 + 2 " and " -x + 2 > 1#

# x > 3 " and " -x + 2 - 2 > 1 - 2#

#x > 3 " and " -x > -1#

Whenever you divide by a #-1# you need to switch the direction of the inequality.

#x > 3 " and " -x/-1 < -1/-1#

#x > 3 " and " x < 1#

When graphing use open holes or parentheses to show #< or >#. Use a solid dot or a bracket to show #<= or >=#

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