Precalculus Examples

Move to the left side of the equation by subtracting it from both sides.
Simplify the left side.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Subtract from to get .
Find all the values where the expression switches from negative to positive by setting each factor equal to and solving.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Solve for each factor to find the values where the absolute value expression goes from negative to positive.
Find the domain of .
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Set up the equation to solve for .
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.
Simplify.
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Simplify the expression.
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Multiply by to get .
Add and to get .
Simplify each term.
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Dividing two negative values results in a positive value.
Multiply by to get .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by to get .
Subtract from to get .
The left side is greater than the right side , which means the given statement is 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.
Simplify.
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Simplify the expression.
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Multiply by to get .
Add and to get .
Simplify each term.
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Divide by to get .
Multiply by to get .
Subtract from to get .
The left side is less than the right side , which means 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.
Simplify.
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Simplify the expression.
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Multiply by to get .
Add and to get .
Simplify each term.
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Divide by to get .
Multiply by to get .
Subtract from to get .
The left side is greater than the right side , which means the given statement is true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
The solution consists of all of the true intervals.
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