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**Chapter 2: Equations and Inequalities 2.4: Other Types of Equations**

Essential Question: How many solutions should you expect in an absolute value equation? A radical equation? A fractional equation?

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**2.4: Other Types of Equations**

Solving Absolute Value Equations Get the absolute value term alone on one side of the equation e.g. If you have 3|2x + 5| - 12 = 0, add 12 to both sides of the equation, then divide both sides by to get |2x + 5| = 4 Create two equations and solve for x One positive (like the normal equation, without the | | signs) One negative (flip signs for all terms not inside the | |) 2x + 5 = 4 2x + 5 = -4 Check your answers for extraneous solutions

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**2.4: Other Types of Equations**

Solving Absolute Value Equalities Ex. 2: Using the Algebraic Definition Just like quadratic equations, where taking the square root of both sides left us with a positive or negative solution, removing absolute value requires us to solve for a positive and negative solution. |x + 4| = 5x – 2 or

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**2.4: Other Types of Equations**

Ex. 3: Solving an Absolute Value Quadratic Equation Solve |x2 + 4x – 3| = 2 or

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**2.4: Other Types of Equations**

Page 116 9-21, all problems

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**Chapter 2: Equations and Inequalities 2**

Chapter 2: Equations and Inequalities 2.4: Other Types of Equations Day 2 Essential Question: How many solutions should you expect in an absolute value equation? A radical equation? A fractional equation?

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**2.4: Other Types of Equations**

Solving Radical Equations Radical equations are equations that use a radical (root) symbol. Graphing radical equations will only generate approximate solutions. Exact solutions need to be found algebraically. To remove a radical (Power principle) isolate the radical take each side to the inverted power e.g. square root → square both sides e.g. cube root → cube both sides) Squaring both sides of an equation may introduce extraneous solutions, so solutions to radical equations MUST be checked in the original equation

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**2.4 Other Types of Equations**

Ex. 4: Solving a Radical Equation Solve isolate the radical square both sides FOIL the right Get equation =0 Factor x = 9 or x = 4 √ Solutions

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**2.4: Other Types of Equations**

Sometimes the power principle must be applied twice Ex. 5: Solve

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**2.4: Other Types of Equations**

Ex 5 (continued), 2nd application Square both sides FOIL left square each on right Distribute Get one side = 0 Factor √ extraneous solutions

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**2.4: Other Types of Equations**

Fractional Equations If f(x) and g(x) are algebraic expressions, the quotient is called a fractional expression with numerator f(x) and denominator g(x). As in all fractions, the denominator, g(x), cannot be zero. That is, if g(x) = 0, the fraction is undefined. To solve a fractional equation: Solve the numerator Plug all answers in the denominator to avoid extraneous roots

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**2.4: Other Types of Equations**

Ex. 7: Solving a Fractional Equation Solve Find all solutions to 6x2 – x – 1 = 0

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**2.4: Other Types of Equations**

Check your solutions of x=½ and x=-⅓ Plug your answers from the numerator into the denominator (2x2 + 9x – 5) -⅓ is a solution, and ½ is extraneous

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**2.4: Other Types of Equations**

Assignment Page 116 – 117 29 – 41 & 49 – 63 Odd problems (show work)

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