Power of a Power Property of Exponents
Adding and Subtracting Rational Numbers
Solving Equations with Radicals and Exponents
Quadratic Equations
Using Intercepts for Graphing Linear Equations
Graphing Linear Equations in Two
Multiplying Fractions
Solving Linear Equations Containing Fractions
Evaluating Polynomials
Multiplication Property of Square and Cube  Roots
Writing a Fraction in Simplest Form
Square Roots
The Pythagorean Theorem
Factoring The Difference of 2 Squares
Solving Polynomial Equations
Roots and Powers
Writing Linear Equations in Standard Form
Solving Nonlinear Equations by Substitution
Straight Lines
The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

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Solving Equations

You will generally find the last operation is the first thing to undo. Imagine you are computing the equation on a calculator. The last operation you would type is likely to be the first operation to undo. Let’s look at a really big and messy example; try to spot how we’re working backwards to undo it!

Big Messy Example:

Solve for x: 2(x - 1)2 + 3 = 21


Subtract 3 from both sides: 2(x - 1)2 + 3 - 3 = 21 - 3
or: 2(x - 1)2 = 18
Divide both sides by 2:
or: (x - 1)2 = 9
Square root of both sides:
or: x - 1 = 3
Finally add 1 to both sides: x + 1 - 1 = 3 + 1
 or: x = 4


Substitute 4 into the original equation:

2•(4-1)2 + 3 = 21

2•32 + 3 = 21

2•9 + 3 = 21

21 = 21 Yes!