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	Simplifying Complex Fractions 1
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	Collecting Like Terms
	Solving Equations with Radicals and Exponents
	Percent of Change
	Powers of ten (Scientific Notation)
	Comparing Integers on a Number Line
	Solving Systems of Equations Using Substitution
	Factoring Out the Greatest Common Factor
	Families of Functions
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	Multiplying and Dividing Complex Numbers
	Properties of Exponents
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	Radicals
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	The Quadratic Formula
	Writing a Quadratic with Given Solutions
	Simplifying Square Roots
	Adding and Subtracting Square Roots
	Adding and Subtracting Rational Expressions
	Combining Like Radical Terms
	Solving Systems of Equations Using Substitution
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	Product of a Sum and a Difference
	Solving First Degree Inequalities
	Solving Equations with Radicals and Exponents
	Roots and Powers
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Solving Equations with Radicals and Exponents

Raising Each Side to a Power

Example 1

Raising each side to a power to eliminate radicals

Solve each equation.

a)		Original equation
		Cube each side.
3x + 5	= x - 1
2x	= -6
x	= -3

Check x = -3 in the original equation:

Note that is a real number. The solution set is {-3}. In this example we checked for arithmetic mistakes. There was no possibility of extraneous solutions here because we raised each side to an odd power.

b)	= x				Original equation
3x + 18	= x²				Square both sides.
-x² + 3x + 18	= x²				Simplify.
x² - 3x - 18	= 0				Subtract x² from each side to get zero on one side.
(x - 6)(x + 3)	= 0				Multiply each side by -1 for easier factoring.
x - 6	= 0				Factor.
x	= 0	or	x + 3	= 0	Zero factor property
	= 6	or	x	= -3

Because we squared both sides, we must check for extraneous solutions. If x = -3 in the original equation , we get

which is not correct. If x = 6 in the original equation, we get which is correct. The solution set is {6}.