How do you solve the inequality #|3x-2| + 4<= 7#?

Question

3304 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-12T06:10:57

The solution is #x in [-1/3,5/3]#

The inequality is

#|3x-2|+4<=7#

#|3x-2|<=7-4<=3#

Therefore,

#{(3x-2<=3),(-3x+2<=3):}#

#<=>#, #{(3x<=5),(3x>=-1):}#

#<=>#, #{(x<=5/3),(x>=-1/3):}#

The solution is

#x in [-1/3,5/3]#

graph{|3x-2|-3 [-5.55, 5.55, -2.772, 2.777]}