SOLUTION: 5|x+4|< 10 - 5, x+4 in absolute value is less than or equal to 10

Algebra ->  Absolute-value -> SOLUTION: 5|x+4|< 10 - 5, x+4 in absolute value is less than or equal to 10      Log On


   

Question 131396This question is from textbook
: 5|x+4|< 10
-
5, x+4 in absolute value is less than or equal to 10 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2Aabs%28x%2B4%29%3C=10 Start with the given inequality


abs%28x%2B4%29%3C=2 Divide both sides by 5



Break up the absolute value (remember, if you have abs%28x%29%3C=+a, then x+%3E=+-a and x+%3C=+a)

x%2B4+%3E=+-2 and x%2B4+%3C=+2 Break up the absolute value inequality using the given rule


-2+%3C=+x%2B4+%3C=+2 Combine the two inequalities to get a compound inequality



-6+%3C=+x+%3C=+-2 Subtract 4 from all sides


----------------------------------------------------

Answer:

So our answer is

-6+%3C=+x+%3C=+-2



which looks like this in interval notation





if you wanted to graph the solution set, you would get

Graph of the solution set in blue and the included values represented by closed circles