SOLUTION: Please Help, 7|z+6|+8 is less than or equal to 57, I think the answer is less than or equal to 1 but i'm really not sure

Algebra ->  Absolute-value -> SOLUTION: Please Help, 7|z+6|+8 is less than or equal to 57, I think the answer is less than or equal to 1 but i'm really not sure      Log On


   



Question 80013: Please Help,
7|z+6|+8 is less than or equal to 57, I think the answer is less than or equal to 1 but i'm really not sure

Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
7|z+6|+8<=57
You are close, but you are missing a key point... first, manipulate the equation to get the absolute value alone on one side:
7|z+6|<=49
|z+6|<=7
Given the inequality |x|<= a, the solution is always of the form –a <=x<= a. So now you can get rid of those pesky absolute value symbols and rewrite the equation like this:
-7%3C=z%2B6%3C=7
This is now something that you can deal with... solve for z by subtracting 6 from each term and you are done.
highlight%28-13%3C=z%3C=1%29
So you can see how you only got this problem half right. You can confirm the answer by plugging it into the original inequality.