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Course: College Algebra
Topic: Equations and Inequalities
Subtopic: Advanced Equations

Overview

The goal of today's lesson is to solve a variety of equations building on solving skills from elementary and intermediate algebra but kicked up a notch in difficulty in preparation for calculus. Practice solving all types of equations including polynomial, rational, radical, fractional exponent, and absolute value. Your concentration should be on solving equations algebraically, but you should also be able to solve graphically using technology as needed. "Checking" your algebraic answers by electronically graphing is great practice!

Caution: When solving equations that contain a radical or fractional exponent, if the solving process requires even-powering both sides of the equation, extraneous solutions are possible thus you must CHECK your answers.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 1.1.1 Algebraically solve polynomial equations by factoring, quadratic formula, etc.
• 1.1.2 Algebraically solve equations containing radicals, fractional exponents, or absolute values
• 1.1.3 Solve equations using a substitution
• 1.1.4 Recognize when a substitution is useful and when it is not
• 1.1.5 Recognize extraneous solutions both algebraically and graphically
• 1.1.6 Solve equations graphically using an electronic grapher and its zero or intersection command

Terminology

Define: polynomial equation, quadratic equation, radical equation, fractional exponent equation, absolute value equation, extraneous solution

Text Notes

Many texts over-use the "substitution" method to rewrite an equation. Look for more direct ways to solve including factoring with fractional exponents or radicals as these processes will serve you well in calculus.

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U - Algebra 1 and search for the term "Solving Equations in Quadratic Form".

More examples can be found at MathIsPower4U - Algebra 2 and searching for the topics "Solving Radical Equations' and "Solving Rational Equations" both of which include some easier equations from Intermediate Algebra as review and some more advanced equations such as the ones we cover here in College Algebra.