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Precalculus Examples
Step 1
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2
Step 2.1
Set equal to .
Step 2.2
Subtract from both sides of the equation.
Step 3
Step 3.1
Set equal to .
Step 3.2
Solve for .
Step 3.2.1
Add to both sides of the equation.
Step 3.2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.2.3
Simplify .
Step 3.2.3.1
Rewrite as .
Step 3.2.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.2.4
The complete solution is the result of both the positive and negative portions of the solution.
Step 3.2.4.1
First, use the positive value of the to find the first solution.
Step 3.2.4.2
Next, use the negative value of the to find the second solution.
Step 3.2.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 4
Step 4.1
Set equal to .
Step 4.2
Solve for .
Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Divide each term in by and simplify.
Step 4.2.2.1
Divide each term in by .
Step 4.2.2.2
Simplify the left side.
Step 4.2.2.2.1
Dividing two negative values results in a positive value.
Step 4.2.2.2.2
Divide by .
Step 4.2.2.3
Simplify the right side.
Step 4.2.2.3.1
Divide by .
Step 5
The final solution is all the values that make true.
Step 6
Use each root to create test intervals.
Step 7
Step 7.1
Test a value on the interval to see if it makes the inequality true.
Step 7.1.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 7.1.2
Replace with in the original inequality.
Step 7.1.3
The left side is less than the right side , which means that the given statement is false.
False
False
Step 7.2
Test a value on the interval to see if it makes the inequality true.
Step 7.2.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 7.2.2
Replace with in the original inequality.
Step 7.2.3
The left side is greater than the right side , which means that the given statement is always true.
True
True
Step 7.3
Test a value on the interval to see if it makes the inequality true.
Step 7.3.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 7.3.2
Replace with in the original inequality.
Step 7.3.3
The left side is less than the right side , which means that the given statement is false.
False
False
Step 7.4
Test a value on the interval to see if it makes the inequality true.
Step 7.4.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 7.4.2
Replace with in the original inequality.
Step 7.4.3
The left side is greater than the right side , which means that the given statement is always true.
True
True
Step 7.5
Test a value on the interval to see if it makes the inequality true.
Step 7.5.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 7.5.2
Replace with in the original inequality.
Step 7.5.3
The left side is less than the right side , which means that the given statement is false.
False
False
Step 7.6
Compare the intervals to determine which ones satisfy the original inequality.
False
True
False
True
False
False
True
False
True
False
Step 8
The solution consists of all of the true intervals.
or
Step 9
Convert the inequality to interval notation.
Step 10