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Chapter 1 - Fundamentals 1.5 - Equations

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Definitions Equation An equation is a statement that two mathematical statements are equal. Solutions The values of the unknown that make the equation true are called the solutions or roots of the equation. 1.5 - Equations

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Definitions Solving the equation The process of finding the solutions is called solving the equation. Equivalent Equations Two equations with exactly the same solutions are called equivalent equations. 1.5 - Equations

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Definitions Linear Equations A linear equation in one variable is an equation equivalent to one of the form where a and b are real numbers and x is the variable. 1.5 - Equations

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Definitions Literal Equations Equations with several variables (letters) are called literal equations. Even though there are more letters in these equations, the methods used to solve these equations are the same as the methods you use to solve all equations. 1.5 - Equations

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Example 1 – pg. 55 #32 Solve the equation for the indicated variable. 1.5 - Equations

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Definitions Quadratic Equations A quadratic equation is an equation of the form where a, b, and c are real numbers with a 0. 1.5 - Equations

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Solving Quadratic Equations What are three methods of solving quadratic equations? 1.5 - Equations

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Quadratic Formula The roots of the quadratic equation where a 0, are 1.5 - Equations

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Example 2 – pg. 55 Solve the equations. 47. 54. 70. 1.5 - Equations

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Fractional Equations To solve fractional expressions we must 1. Factor the numerator and denominator completely. 2. State the restrictions or domain. 3. Eliminate the denominator by multiplying each term by the LCD. 4. Expand and combine like terms. 5. Move all terms to one side of = sign. 6. Solve the quadratic. 7. Check your solutions. 1.5 - Equations

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Example 3 – pg. 55 #86 Find all real solutions of the equation. 1.5 - Equations

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Radical Equations When we solve radical equations, we must be careful to check your final answers. We may end up with an extraneous solution, a solution that does not satisfy the original equation. 1.5 - Equations

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Example 4 – pg. 55 #91 Find all real solutions of the equation. 1.5 - Equations

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Algebraic Expression An equation of the form where W is an algebraic expression, is an equation of quadratic type. We solve equations of quadratic type by substituting for the algebraic expression, as we see in the next two examples. 1.5 - Equations

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Example 5 – pg. 55 #97 Find all real solutions of the equation. 1.5 - Equations

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Example 6 – pg. 55 #100 Find all real solutions of the equation. 1.5 - Equations

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