SOLUTION: Solve 4|3x|-5 is less than or equal to 5

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Question 173314This question is from textbook Saxon Algebra 2
: Solve 4|3x|-5 is less than or equal to 5 This question is from textbook Saxon Algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4%2Aabs%283x%29-5%3C=5 Start with the given inequality


4%2Aabs%283x%29%3C=10 Add 5 to both sides.


abs%283x%29%3C=10%2F4 Divide both sides by 4


abs%283x%29%3C=5%2F2 Reduce



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

3x+%3E=+-5%2F2 and 3x+%3C=+5%2F2 Break up the absolute value inequality using the given rule


-5%2F2+%3C=+3x+%3C=+5%2F2 Combine the two inequalities to get a compound inequality


-%285%2F2%29%2F3+%3C=+x+%3C=+%285%2F2%29%2F3 Divide all sides by 3 to isolate x


-5%2F6+%3C=+x+%3C=+5%2F6 Reduce



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Answer:

So our answer is

-5%2F6+%3C=+x+%3C=+5%2F6




So the answer in interval notation is []


Also, the answer in set-builder notation is