SOLUTION: Solve the following inequality and list your solution using interval notation: |-3x � 5|

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Question 115273: Solve the following inequality and list your solution using interval notation:
|-3x � 5| > 10

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

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Answer:

So our answer is

or

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 excluded values represented by open circles

SOLUTION: Solve the following inequality and list your solution using interval notation: |-3x � 5| > 10