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

for this inequality we can start with:

Now we solve both inequalities:

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

Now combine the inequalities:

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

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

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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.

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.

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.

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