SOLUTION: Solve |x+4|<7 the answer is -11<x<3 I know the answer because its in my summer homework but I don't get how to solve it. Thank you for your help if you help me.

Question 980855: Solve |x+4|<7
the answer is -11 I know the answer because its in my summer homework but I don't get how to solve it.
Thank you for your help if you help me.
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
You cannot know that the answer is -11, because you have an inequality using absolute value, so you will have a set of x values; NOT just a single x value.

Think how abs(x+4) will be related to the 7 on a number line. Either x+4 is less than 7, or -x-4 is greater than -7. Solve for both conditions.

For x+4 POSITIVE or ZERO,

BUT
For x+4 NEGATIVE,

---------think about this step very carefully to understand;

Put the two results together:
.
Solutions for x are between negative eleven and positive three, EXCLUSIVE.
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