How do you graph and solve #-½ |6-4x| +2 ≤ 1 #?

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Answer 1 · 2018-06-22T16:28:24

The solution is #x in (-oo,1]uu [2, +oo)#

The inequality is

#-1/2|6-4x|+2<=1#

#-1/2|6-4x<=1-2#

#-1/2|6-4x|<=-1#

#|6-4x|>=2#

Therefore,

#{(6-4x>=2),(-6+4x>=2):}#

#<=>#, #{(4x<=4),(4x>=8):}#

#<=>#, #{(x<=1),(x>=2):}#

The solution is

#x in (-oo,1]uu [2, +oo)#

graph{-1/2|6-4x|+2-1 [-8.89, 8.89, -4.444, 4.445]}