Trigonometry Examples

Convert to Interval Notation |5x-5|<-15
Remove the absolute value term. This creates a on the right side of the inequality because .
Set up the positive portion of the solution.
Solve the first inequality for .
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Move all terms not containing to the right side of the inequality.
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Add to both sides of the inequality.
Add and .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
Set up the negative portion of the solution. When solving the negative portion of an inequality, flip the direction of the inequality sign.
Solve the second inequality for .
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Move all terms not containing to the right side of the inequality.
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Add to both sides of the inequality.
Add and .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
Set up the intersection.
and
Since the left side is always positive, the inequality has no solution over the domain.
No solution
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