How do you solve #abs(1-2x)>=13#?

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Answer 1 · 2017-04-13T16:47:31

#x <= -6, x >= 7#

#|1-2x| >= 13# needs to be broken into two problems:

#+(1-2x) >=13 " and " -(1-2x)>= 13#

Solve each equation. Start with the positive equation:

#1-2x >=13#

Subtract #1# on both sides:
#-2x >= 12#

Divide by #-2#, be sure to flip the > to < because of the negative:
#x <= -6#

Solve the negative equation:
#-(1-2x)>= 13#

Distribute the #-1#:
#-1 + 2x >= 13#

Add #1# to both sides:
#2x >= 14#

Divide by #2# on both sides:
#x >= 7

Answer: #x <= -6, x >= 7#