SOLUTION: Solve the following inequality and list solution in interval notation. |-3x-5|≥10 Can someone help me with this question, please. Thank you

Algebra ->  Absolute-value -> SOLUTION: Solve the following inequality and list solution in interval notation. |-3x-5|≥10 Can someone help me with this question, please. Thank you      Log On


   

Question 166106: Solve the following inequality and list solution in interval notation.
|-3x-5|≥10
Can someone help me with this question, please. Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28-3x-5%29%3E=10 Start with the given inequality


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

-3x-5+%3C=+-10 or -3x-5+%3E=+10 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality -3x-5+%3C=+-10


-3x-5%3C=-10 Start with the given inequality


-3x%3C=-10%2B5Add 5 to both sides


-3x%3C=-5 Combine like terms on the right side


x%3E=%28-5%29%2F%28-3%29 Divide both sides by -3 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



x%3E=5%2F3 Reduce


Now lets focus on the second inequality -3x-5+%3E=+10


-3x-5%3E=10 Start with the given inequality


-3x%3E=10%2B5Add 5 to both sides


-3x%3E=15 Combine like terms on the right side


x%3C=%2815%29%2F%28-3%29 Divide both sides by -3 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



x%3C=-5 Divide



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Answer:

So our answer is

x+%3E=+5%2F3 or x+%3C=+-5


So the solution in interval notation is: (] [)


So the solution in set builder notation is:




Here's the graph of the solution set




Note:
There is a closed circle at x=-5 which means that we're including that value from the solution set.


Also, there is a closed circle at x=5%2F3 which means that we're including that value from the solution set.