How do you solve and write the following in interval notation: #|x + 5| <18#?

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Answer 1 · 2016-09-19T12:56:39

#(-23,13)#

#abs(x+5)<18#

Write as two inequalities:

#x+5<18# and #color(white)(aaa)x+5> -18#

#color(white)(a)-5color(white)(a)-5color(white)(aaaaaaaa)-5color(white)(aaaa)-5#

#x<13color(white)(aaaa)#and#color(white)(aaaaaa)x> -23#

In interval notation: #(-23,13)#

Another way to look at it:

Write as one inequality:

#-18< x+5<18#
#-5color(white)(aaaaa)-5color(white)(a)-5#

#-23 < color(white)(aa)x color(white)(aa)< 13#

Interval notation is easier to write when the problem is solved this way because the #x# is "between" the numbers in the interval.
#(-23,13)#