How do you graph and solve #3|8-x| + 2 <7- 2|x-8|#?

Question

1211 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-04T16:12:40

#7<=x<=9#

The graph is all the area between and including x =7 ; x=9

Given: #3|8-x|+2<7-2|x-8|#

Collecting like terms

#3|8-x|+2|x-8|<7-2#

But #|8-x| = |x-8| -> test->|8-2|=|2-8 | -> 6=6#

using only #|8-x|# for both

Factoring out gives:

#|8-x|(3+2)<5#

#|8-x|<1#

Absolute is always 'not negative' so we need:

#0<=|8-x|<1#

If #x = 9" then "|8-x|=1#
If #x>9" then "|8-x|>1#
If #x=7" then "|8-x|=1#
If #x<7" then "|8-x|>1#

So #color(white)(.)7<=x<=9#