Trigonometry Examples

Convert to Interval Notation x-8/x<2
Find the LCD of the terms in the equation.
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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
The LCM is the smallest number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Multiply each term by and simplify.
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Multiply each term in by in order to remove all the denominators from the equation.
Simplify each term.
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Multiply by .
Cancel the common factor of .
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Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Subtract from both sides of the inequality.
Convert the inequality to an equation.
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Set equal to and solve for .
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Set the factor equal to .
Add to both sides of the equation.
Set equal to and solve for .
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Set the factor equal to .
Subtract from both sides of the equation.
Consolidate the solutions.
Find the domain of .
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Set the denominator in equal to to find where the expression is undefined.
The domain is all values of that make the expression defined.
Interval Notation:
Interval Notation:
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
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Test a value on the interval to see if it makes the inequality true.
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Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is less than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
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Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not less than the right side , which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
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Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is less than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not less than the right side , which means that the given statement is false.
False
False
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
False
True
False
True
False
The solution consists of all of the true intervals.
or
Convert the inequality to interval notation.
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