How do you solve and write the following in interval notation: #| x – 3 | < 9#?

1 Answer
Jim G.
Jan 21, 2018

#-6,12)#

Explanation:

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

#"always have solutions of the form "#

#-a < x < a#

#rArr-9 < x-3 <9#

#"add 3 to each of the three intervals"#

#-9color(red)(+3) < xcancel(-3)cancel(color(red)(+3))<9color(red)(+3)#

#rArr-6 < x < 12" is the solution"#

#rArr(-6,12)larrcolor(blue)"in interval notation"#

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