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

1 Answer
Jan 2, 2018

Answer:

#-14<=x<=4#

Explanation:

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#