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Solving Absolute Value Equations, Quadratic (Polynomial), and Rational Inequalities using Sign Charts

Free math notes on solving absolute value equations and polynomial (including quadratic) and rational inequalities using a sign chart.
Notes:
   1.  Absolute Value Equations
   2.  Absolute Value Inequalities
   3.  Quadratic Inequalities
   4.  Polynomial and Rational Inequalities

YouTube Videos: Click on a problem to see it worked out in YouTube.

Absolute Value Equations:












Absolute Value Inequalities












Quadratic Inequalities:








Polynomial and Rational Inequalities












Linear Inequalities (one variable)

Solve and graph the solution set. 
(I.N. stands for interval notation here.)


Compound inequalities can be split up or solved in one step like the following examples. Note that all inequality symbols face the same direction when combined.





Average Problem: Clint wishes to earn a B which is an average of at least 80 but not more than 90.  What range must he score on the fourth exam if the first three were 65, 75, and 90?
Commission Problem: Bill earns $12.00 plus $0.25 for every person he gets to register to vote. How many people must he register to earn at least $50.00 for the day?
Video Examples on YouTube: