How do you solve and write the following in interval notation: # | 3x – 2 | ≥ 4#?
1 Answer
Feb 19, 2017
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"#
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)#
