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

Answer 1

Eli Assouline

#-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#

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Answer 2

Isaiah Anthony

To rewrite the inequality (|x+5| \leq 9) as a compound inequality:

[ -9 \leq x+5 \leq 9 ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

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