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.

Algebra ->  Inequalities -> 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.       Log On


   

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) About Me  (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,
x%2B4%3C7
x%3C7-4
highlight_green%28x%3C3%29
BUT
For x+4 NEGATIVE,
abs%28x%2B4%29%3C7
-x-4%3C7---------think about this step very carefully to understand;
-x-4%2Bx%3C7%2Bx
-4%3C7%2Bx
-4-7%3C7%2Bx-7
highlight_green%28-11%3Cx%29
x%3E-11

Put the two results together:
highlight%28-11%3Cx%3C3%29.
Solutions for x are between negative eleven and positive three, EXCLUSIVE.