Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 6a - Exponents and Rational Functions Mini-Lesson SOLVE RATIONAL EQUATIONS ALGEBRAICALLY To solve rational equations algebraically (also called symbolically): Identify the common denominator for all fractions in the equation. Clear the fractions by multiplying both sides of the equation by the common denominator Take note of the values of x that make the common denominator zero. These x-values cannot be used as solutions to the equation since we cannot divide by 0. Solve for x. Check your work by plugging the value(s) back into the equation or by graphing. Problem 8 WORKED EXAMPLE – SOLVE RATIONAL EQUATIONS ALGEBRAICALLY 3 Solve 5x 4 algebraically. Round solutions to two decimal places. x 4 Common denominator for all sides is x-4. Multiply both sides of the equation by (x – 4) and solve for x to get the following: 3 (5x)( x 4) (4 )( x 4) x 4 2 3 5x 20x 4( x 4) ( x 4) x 4 2 5x 20x 4x 16 3 5x 2 20x 4x 13 0 5x 2 5x 2 20x 4x 13 24x 13 0 Notice that we now have a quadratic equation, which can be solved using the methods of last chapter. Because we are asked to solve our original problem algebraically, let’s continue that process and not resort to a graphical solution. We will use the Quadratic Formula with a=5, b=- 24, and c=13 to get: ( 24) x ( 24) 2(5) 2 4(5)(13) 24 576 260 10 24 316 10 Because we want rounded solutions, I do NOT need to continue reducing my fraction solutions above but can compute the following directly: 24 316 24 316 x 4.18, x .62 10 10 These solutions match what we found in the graphing example previously. To check, plug the values back into the original equation (one at a time) or use the graphing method. Scottsdale Community College Page 250 Intermediate Algebra
Lesson 6a - Exponents and Rational Functions Mini-Lesson Problem 9 MEDIA EXAMPLE – SOLVING RATIONAL EQUATIONS ALGEBRAICALLY Solve 3x 3 1 x 1 algebraically. Round answer(s) to two decimals as needed. Problem 10 YOU TRY – SOLVING RATIONAL EQUATIONS GRAPHICALLY/ALGEBRAICALLY 5 Solve 4 algebraically and graphically. Round answer(s) to two decimals as needed. x 2 Show complete work in this space. Scottsdale Community College Page 251 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 4b - More on Logarithms This
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Intermediate Algebra – Student Workbook – Second Edition 2013

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