How do you solve #abs(2x-3)<=3#?

1 Answer
Jim G.
Apr 11, 2018

#0<=x<=3#

Explanation:

#"inequalities of the type "|x|<=a#

#"always have solutions of the form"#

#-a<=x<=a#

#rArr-3<=2x-3<=3#

#"add 3 to each interval"#

#cancel(-3)cancel(+3)<=2xcancel(-3)cancel(+3)<=3+3#

#rArr0<=2x<=6#

#"divide each interval by 2"#

#rArr0<=x<=3" is the solution"#

#x in[0,3]larrcolor(blue)"in interval notation"#

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