How do you solve and write the following in interval notation: # | 3x – 2 | ≥ 4#?

1 Answer
Feb 19, 2017

Answer:

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

Explanation:

The starting premise is.

#|x|>=a#

#rArrx>=a" or "x<=-a#

#"Applying to "|3x-2|>=4#

#rArr3x-2>=4" or "3x-2<=-4#

Solve each inequality.

#color(blue)"First inequality"#

#3x-2>=4#

add 2 to both sides.

#3xcancel(-2)cancel(+2)>=4+2#

#rArr3x>=6#

divide both sides by 3

#(cancel(3) x)/cancel(3)>=6/3#

#rArrcolor(red)(x>=2)larr" solution"#

#color(blue)"Second inequality"#

#3x-2<=-4#

add 2 to both sides.

#rArr3x<=-2#

#rArrcolor(red)(x<=-2/3)larr" solution"#

The combined solution is #x>=2" or " x<=-2/3#

#"Expressed in interval notation as"#

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