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Section 5.5.notebook 1 January 16, 2018 Solving Rational Equations and Inequalities (Section 5.5)

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Page 1: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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January 16, 2018

Solving Rational Equations and Inequalities(Section 5.5)

Page 2: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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January 16, 2018

Objectives:

~ Solve rational equations and inequalities

Page 3: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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January 16, 2018

Try this:

Page 4: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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What is a rational equation?A rational equation is an equation that contains one or more rational expressions. The time t in hours that it takes to travel d miles can be determined by using the equation t = d/r , where r is the average rate of speed. This equation is a rational equation.

Page 5: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

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Big Hint!To solve a rational equation, multiply each and every term by the LCD.

This eliminates denominators! Much easier!

Page 6: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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Well, Let's Jump Right In!Solve the equations: Make sure to CHECK your answer(s)!

Page 7: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

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Your Turn!Solve each equation.

Page 8: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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Word Problem (Yay!)A kayaker spends an afternoon paddling on a river. She travels 3 mi upstream and 3 mi downstream in a total of 4 hours. In still water, the kayaker can travel at an average speed of 2mi/h. Based on this information, what is the average speed of the river's current? Is your answer reasonable?

Page 9: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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January 16, 2018

More!

Page 10: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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Rational Inequalities!A rational inequality is an inequality that contains one or more rational expressions.

Can be solved by graphing which we will see next block!

You can also solve rational inequalities algebraically. You start by multiplying each term by the least common denominator (LCD) of all the expressions in the inequality. However, you must consider two cases: the LCD is positive or the LCD is negative.

Page 11: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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Solving Rational Inequalities Algebraically

Case I: Positive Case II: Negative

Page 12: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

Section 5.5.notebook

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January 16, 2018

Case I: Positive Case II: Negative

Solve the inequality algebraically

Page 13: Solving Rational Equations and Inequalities (Section 5.5) · ~ Solve rational equations and inequalities. Section 5.5.notebook 3 January 16, 2018 Try this: Section 5.5.notebook 4

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Pop Problem!

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