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How do you solve and write the following in interval notation: #| 3 − 2x | − 8 ≥ 1#?

1 Answer

Shwetank Mauria

May 29, 2016

#x<=-3# or #x>=6#

Explanation:

#|3-2x|-8>=1# means #|3-2x|>=9#

Now #|a|>=b# means either #a>=b# or #-a>=b#

Hence, #|3-2x|>=9# means

either #3-2x>=9# i.e. #-2x>=9-3# or #-2x>=6# i.e. #x<=-3#

or #-(3-2x)>=9# i.e. #-3+2x>=9# or #2x>=12# i.e. #x>=6#

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