1. Boundless Lecture Slides Free to share, print, make copies and changes. Get yours at www.boundless.com Available on the Boundless Teaching Platform

2. Using Boundless Presentations The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: If you have any questions or problems please email: educators@boundless.com http://boundless.com/teaching-platform

3. Boundless is an innovative technology company making education more affordable and accessible for students everywhere. The company creates the world’s best open educational content in 20+ subjects that align to more than 1,000 popular college textbooks. Boundless integrates learning technology into all its premium books to help students study more efficiently at a fraction of the cost of traditional textbooks. The company also empowers educators to engage their students more effectively through customizable books and intuitive teaching tools as part of the Boundless Teaching Platform. More than 2 million learners access Boundless free and premium content each month across the company’s wide distribution platforms, including its website, iOS apps, Kindle books, and iBooks. To get started learning or teaching with Boundless, visit boundless.com.boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com About Boundless

4. Rational Equations Radical Equations Equations with Absolute Value Further Equation-Solving Functions, Equations, and Inequalities > Further Equation-Solving Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_26&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. You can have multiple values that will satisfy the equations. It is important to check your work to make sure that all the values you find all work for the equations. If you have a rational equation where the denominators are the same, then the numerators must be the same.This gives us a strategy: Find a common denominator, and then set the numerators equal. It is important to write each equation in its simplest form. This means to factor each problem out as much as you possibly can before starting. Rational Equations Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/further-equation-solving-26/rational- equations-136- 7359?campaign_content=book_196_section_26&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Functions, Equations, and Inequalities > Further Equation-Solving

6. When solving equations that involve radicals, begin by asking: is there an x under the square root? The answer to this question will determine the way you approach the problem. If there is not an x under the square root—if only numbers are under the radicals—the problem can be solved much the same way as if it had no radicals. However, if there is an x under a square root, then move everything except the radical to one side, then square both sides. Squaring both sides can introduce false answers—so it is important to check the answers after solving! Radical Equations Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/further-equation-solving-26/radical- equations-137- 6107?campaign_content=book_196_section_26&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Functions, Equations, and Inequalities > Further Equation-Solving

7. Absolute value is one of the simplest functions—and paradoxically, one of the most problematic. On the face of it, nothing could be simpler: it just means "whatever comes in, a positive number comes out". In order to solve an absolute value equation: 1) Isolate the absolute value algebraically. 2) Think through the problem. That is to say, set the absolute value term equal to the other side of the equation, then the opposite of the other side (-1 times it). 3) Finally, do more algebra to isolate x. Absolute values are always positive. An absolute value equation can have, at most, two solutions. Equations with Absolute Value Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/functions-equations-and-inequalities-3/further-equation-solving-26/equations- with-absolute-value-138- 6676?campaign_content=book_196_section_26&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Absolute Value View on Boundless.com Functions, Equations, and Inequalities > Further Equation-Solving

8. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

9. Key terms absolute value For a real number, its numerical value without regard to its sign; formally, -1 times the number if the number is negative, and the number unmodified if it is zero or positive. denominator The number or expression written below the line in a fraction (thus 2 in ½). numerator The number or expression written above the line in a fraction (thus 1 in ½). radical A root (of a number or quantity). rational expression An expression that can be expressed as the quotient of two polynomials. root the number which,when plugged into the equation, will produce a zero. square The second power of a number, value, term or expression. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities

10. Absolute Value The absolute value of a real number may be thought of as its distance from zero. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Absolute value." GNU FDL http://en.wikipedia.org/wiki/Absolute_value View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Absolute_valueView on Boundless.com Functions, Equations, and Inequalities

11. Interactive Graph: Checking Your Work Graph demonstrating the easy mistake when factoring the denominators and having the resulting graphs $y=3x^2-6x$ and $y=4x^2+24x$ Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Checking Your Work." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-checking-your-work View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-checking-your-workView on Boundless.com Functions, Equations, and Inequalities

12. Interactive Graph: Checking Algebraic Solutions Graph of quadratic equation. This graph shows where the given equation is equal to zero. This is equivalent to showing where. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Checking Algebraic Solutions." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-checking-algebraic-solutions View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-checking-algebraic-solutions View on Boundless.com Functions, Equations, and Inequalities

13. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities Solve for x: |x+2|=7. A) x=5 and x=-9 B) x=-5 and x=9 C) x=47 D) x=5

14. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities Solve for x: |x+2|=7. A) x=5 and x=-9 B) x=-5 and x=9 C) x=47 D) x=5

15. Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities Solve for x: |2x-3|-4=3. A) x=2 and x=-5 B) x=3 and x=0 C) x=-2 and x=5 D) x=-3 and x=0

16. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Functions, Equations, and Inequalities Solve for x: |2x-3|-4=3. A) x=2 and x=-5 B) x=3 and x=0 C) x=-2 and x=5 D) x=-3 and x=0

17. Attribution Connexions. "Radical Concepts -- Radical Equations." CC BY 3.0 http://cnx.org/content/m18273/latest/CC BY 3.0http://cnx.org/content/m18273/latest/ Wiktionary. "square." CC BY-SA 3.0 http://en.wiktionary.org/wiki/squareCC BY-SA 3.0http://en.wiktionary.org/wiki/square Wiktionary. "root." CC BY-SA 3.0 http://en.wiktionary.org/wiki/rootCC BY-SA 3.0http://en.wiktionary.org/wiki/root Wiktionary. "radical." CC BY-SA 3.0 http://en.wiktionary.org/wiki/radicalCC BY-SA 3.0http://en.wiktionary.org/wiki/radical Connexions. "Absolute Value Equations." CC BY 3.0 http://cnx.org/content/m18201/latest/?collection=col10624CC BY 3.0http://cnx.org/content/m18201/latest/?collection=col10624 Wiktionary. "absolute value." CC BY-SA 3.0 http://en.wiktionary.org/wiki/absolute+valueCC BY-SA 3.0http://en.wiktionary.org/wiki/absolute+value Connexions. "Rational Equations." CC BY 3.0 http://cnx.org/content/m18302/latest/?collection=col10624CC BY 3.0http://cnx.org/content/m18302/latest/?collection=col10624 Wiktionary. "numerator." CC BY-SA 3.0 http://en.wiktionary.org/wiki/numeratorCC BY-SA 3.0http://en.wiktionary.org/wiki/numerator Wiktionary. "denominator." CC BY-SA 3.0 http://en.wiktionary.org/wiki/denominatorCC BY-SA 3.0http://en.wiktionary.org/wiki/denominator Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//algebra/definition/rational-expressionCC BY-SA 3.0http://www.boundless.com//algebra/definition/rational-expression Free to share, print, make copies and changes. Get yours at www.boundless.com Functions, Equations, and Inequalities