How do you solve #abs(2/3 k - 1)>=2#?

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Answer 1 · 2018-05-21T12:08:13

The solutions are # k in (-oo, -3/2] uu[9/2, +oo)#

This is an inequality with absolute values.

#|2/3k-1|>=2#

The solutions are obtained as follows :

#{(2/3k-1>=2),(-2/3k+1>=2):}#

#<=>#, #{(2/3k>=3),(2/3k<=-1):}#

#<=>#, #{(k>=9/2),(k<=-3/2):}#

The solutions are

# k in (-oo, -3/2] uu[9/2, +oo)#

graph{|2/3x-1|-2 [-6.22, 9.58, -3.73, 4.17]}