# Write the Absolute Value as piecewise |x^3-10x^2|

The piecewise polynomials are when and when .
Remove parentheses.
Solve for when .
Convert the inequality to an equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Set equal to and solve for .
Take the root of both sides of the to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is equal to .
Set equal to and solve for .
Set the factor equal to .
Add to both sides of the equation.
Consolidate the solutions.
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.
Test a value on the interval to see if it makes the inequality true.
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 false.
Test a value on the interval to see if it makes the inequality true.
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 false.
Test a value on the interval to see if it makes the inequality true.
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 greater than the right side , which means that the given statement is always true.
Compare the intervals to determine which ones satisfy the original inequality.

False

False

The solution consists of all of the true intervals.

Combine the intervals.

Simplify .
Apply the distributive property.

Simplify the expression.
Rewrite as .

Multiply by .

Solve for when .
Convert the inequality to an equation.

Factor out of .
Factor out of .

Factor out of .

Factor out of .

Set equal to and solve for .
Take the root of both sides of the to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

is equal to .

Set equal to and solve for .
Set the factor equal to .

Add to both sides of the equation.

Consolidate the solutions.

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.
Test a value on the interval to see if it makes the inequality true.
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.

Test a value on the interval to see if it makes the inequality true.
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.

Test a value on the interval to see if it makes the inequality true.
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.

Compare the intervals to determine which ones satisfy the original inequality.

True

True

The solution consists of all of the true intervals.

Write the Absolute Value as piecewise |x^3-10x^2|

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