# Problem Solving Inequalities

The quadratic formula is a quick way that will allow us to quickly solve any quadratic equation.

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We will give a procedure for determining which method to use in solving quadratic equations and we will define the discriminant which will allow us to quickly determine what kind of solutions we will get from solving a quadratic equation.

Applications of Quadratic Equations – In this section we will revisit some of the applications we saw in the linear application section, only this time they will involve solving a quadratic equation.

Included are examples in distance/rate problems and work rate problems.

Equations Reducible to Quadratic Form – Not all equations are in what we generally consider quadratic equations.

In this section we will solve this type of equation.

Equations with Radicals – In this section we will discuss how to solve equations with square roots in them.All the properties below are also true for inequalities involving ≥ and ≤.The addition property of inequality says that adding the same number to each side of the inequality produces an equivalent inequality $$If \: x\frac$$ To solve a multi-step inequality you do as you did when solving multi-step equations.Take one thing at the time preferably beginning by isolating the variable from the constants.When solving multi-step inequalities it is important to not forget to reverse the inequality sign when multiplying or dividing with negative numbers.Absolute Value Equations – In this section we will give a geometric as well as a mathematical definition of absolute value.We will then proceed to solve equations that involve an absolute value.Quadratic Equations, Part II – In this section we will continue solving quadratic equations.We will use completing the square to solve quadratic equations in this section and use that to derive the quadratic formula.Here is a list of all the sections for which practice problems have been written as well as a brief description of the material covered in the notes for that particular section.Solutions and Solution Sets – In this section we introduce some of the basic notation and ideas involved in solving equations and inequalities.

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