Question 80013
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<=z+6<=7}}}
This is now something that you can deal with... solve for z by subtracting 6 from each term and you are done.
{{{highlight(-13<=z<=1)}}}
So you can see how you only got this problem half right. You can confirm the answer by plugging it into the original inequality.