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# Algebra Examples

Set the radicand in greater than or equal to to find where the expression is defined.

Solve for .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to and solve.

Set the first factor equal to .

Subtract from both sides of the equation.

Set the next factor equal to and solve.

Set the next factor equal to .

Subtract from both sides of the equation.

Multiply each term in by

Multiply each term in by .

Multiply .

Multiply by .

Multiply by .

Multiply by .

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.

False

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.

True

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 false.

False

False

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

False

True

False

False

True

False

The solution consists of all of the true intervals.

The domain is all values of that make the expression defined.

Interval Notation:

Set-Builder Notation:

Interval Notation:

Set-Builder Notation:

Replace the variable with in the expression.

Simplify the result.

Remove parentheses.

Subtract from .

Multiply by .

Add and .

Multiply by .

Rewrite as .

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

The final answer is .

Replace the variable with in the expression.

Simplify the result.

Remove parentheses.

Add and .

Multiply by .

Subtract from .

Multiply by .

Rewrite as .

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

The final answer is .

The end points are .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Remove parentheses.

Subtract from .

Multiply by .

Add and .

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Remove parentheses.

Subtract from .

Multiply by .

Add and .

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Remove parentheses.

Add and .

Multiply by .

Add and .

Multiply by .

Rewrite as .

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

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Remove parentheses.

Add and .

Multiply by .

Subtract from .

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

The final answer is .

Substitute the value into . In this case, the point is .

Replace the variable with in the expression.

Simplify the result.

Remove parentheses.

Add and .

Multiply by .

Subtract from .

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

The final answer is .

The square root can be graphed using the points around the vertex