How do you solve #|12- 5x | < 22#?

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Answer 1 · 2016-09-27T09:45:27

#-2 < x< 34/5#

#|12-5x|<22# means

either #12-5x<22# i.e.

#12-22<5x# i.e.

#5x> -10# i.e. #x> -2#

or #-(12-5x)<22# i.e.

#-12+5x<22# i.e.

#5x< 22+12# i.e. #5x<34# i.e. #x<34/5#

Hence either #x> -2# or #x< 34/5#, which can be combined as

#-2 < x< 34/5#

Answer 2 · 2018-08-04T00:49:16

#-2 < x< 34/5#

This can be interpreted as

#-5x+12<22# and #-5x+12> -22#

We can subtract #12# from both sides in both inequalities to get

#-5x<10# and #-5x> -34#

Next, we can divide both sides by #-5#. Recall the direction of the inequality will flip. We get

#x> -2# and #x< 34/5#

We can combine these to get

#-2 < x < 34/5#

Hope this helps!