SOLUTION: I am having trouble with absolute value in inequalities. What does it mean? The difference between 9 and 3 times the distance between x and -5 is greater than 6. I did try to

Algebra ->  Absolute-value -> SOLUTION: I am having trouble with absolute value in inequalities. What does it mean? The difference between 9 and 3 times the distance between x and -5 is greater than 6. I did try to       Log On


   

Question 933499: I am having trouble with absolute value in inequalities.
What does it mean?
The difference between 9 and 3 times the distance between x and -5 is greater than 6.
I did try to to this. Here's what I think. 9-3|x-5|>6 only question. Is it supposed to be x-5 or x+5? And then i got the answer : -6>x>-4. Your help is greatly appreciated.. As i showed you here I did try but did not get the answer. Also tell me the definition of absolute value and how it is used in word problems if you would not mind.

Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
three times the difference between x & -5 is x-(-5)= (x+5)
9-(x+5)>6

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between 9 and 3 times the distance between x and -5 is greater than 6.


9-3%2Aabs%28x-%28-5%29%29%3E6
9-3%2Aabs%28x%2B5%29%3E6

Continue simplifying.
-3%2Aabs%28x%2B5%29%3E6-9
-3%2Aabs%28x%2B5%29%3E-3
Multiplying both sides by a negative quantity will reverse the inequality direction:
%28-1%2F3%29%28-3%2Aabs%28x%2B5%29%29%3C%28-1%2F3%29%28-3%29
highlight_green%28abs%28x%2B5%29%3C1%29


x+5 could be negative or non-negative. Solve for each case.

Non-negative,
x%2B5%3C1
x%3C-4
If negative,
-x-5%3C1
x%2B5%3E-1
x%3E-1-5
x%3E-6
-
Put those two results together.
highlight%28-6%3Cx%3C-4%29

The meaning of absolute value is how far from 0 on the number line. For more detailed explanations and study, use your textbook. Absolute Value is always a POSITIVE quantity.