How do you solve and graph #abs(10-3x)>=17#?

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Answer 1 · 2018-06-22T12:43:14

The solution is #x in (-oo,-7/3]uu [9,+oo)#

This is an inequality with absolute values

#|10-3x|>=17#

Therefore,

#{(10-3x>=17),(-10+3x>=17):}#

#<=>#, #{(3x<=10-17),(3x>=17+10):}#

#<=>#, #{(x<=-7/3),(x>=9):}#

The solution is

#x in (-oo,-7/3]uu [9,+oo)#

The graph is

graph{|10-3x|-17 [-25.5, 25.83, -17.22, 8.43]}