SOLUTION: I am to Solve this inequality...the actual answer is (-9/5, 1) (didnt know how to make vertical lines but the 5k+2 has vertical lines on each side) {{{5k+2 -3 is less than or e

Algebra ->  Inequalities -> SOLUTION: I am to Solve this inequality...the actual answer is (-9/5, 1) (didnt know how to make vertical lines but the 5k+2 has vertical lines on each side) {{{5k+2 -3 is less than or e      Log On


   

Question 108980: I am to Solve this inequality...the actual answer is (-9/5, 1)
(didnt know how to make vertical lines but the 5k+2 has vertical lines on each side)
5k%2B2+++-3+is+less+than+or+equal+to+4
What I got so far
5k+2 -3 <=4
7k-3<=4
4k-3<=4-3
4k<=1
I was thinking next to take each side divide by 4 but it wasnt working out
Can you please help me find out where I went wrong.
Thank you so much :)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%285k%2B2%29-3%3C=4 Start with the given inequality


abs%285k%2B2%29%3C=7 Add 3 to both sides.


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

5k%2B2+%3E=+-7 and 5k%2B2+%3C=+7 Break up the absolute value inequality using the given rule


-7+%3C=+5k%2B2+%3C=+7 Combine the two inequalities to get a compound inequality



-9+%3C=+5k+%3C=+5 Subtract 2 from all sides


-9%2F5+%3C=+k+%3C=+1 Divide all sides by 5 to isolate k



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Answer:

So our answer is

-9%2F5+%3C=+k+%3C=+1



which looks like this in interval notation




note: since the inequality was less than or equal to, that means the end points are included. So that is why brackets are used instead of parenthesis.