How do you rewrite the inequality #abs(x+5)<=9# as a compound inequality?

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Answer 1 · 2018-01-02T08:47:06

#-14<=x<=4#

for this inequality we can start with:

#|x+5|<=9# so both of the following are true:
If #x+5# is positive: #x+5<=9#
If #x+5# is negative: #-(x+5)<=9#

Now we solve both inequalities:

#x+5<=9\rightarrow x <=4#

The second inequality is a little more difficult. Remember if you divide by a negative you must change the direction of the inequality:

#-(x+5)<=9#

#x+5>=-9#

#x>=-14#

Now combine the inequalities:

#-14<=x<=4#