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

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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)   (Show Source): You can put this solution on YOUR website!
Start with the given inequality


Break up the absolute value (remember, if you have , then or )

or Break up the absolute value inequality using the given rule




Now lets focus on the first inequality


Start with the given inequality


Add 5 to both sides


Combine like terms on the right side


Divide both sides by -3 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



Reduce


Now lets focus on the second inequality


Start with the given inequality


Add 5 to both sides


Combine like terms on the right side


Divide both sides by -3 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



Divide



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

Answer:

So our answer is

or


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 which means that we're including that value from the solution set.


Also, there is a closed circle at which means that we're including that value from the solution set.
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