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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 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
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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 ect&utm_source=boundless
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 equations ?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
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 equations ?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
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 with-absolute-value ?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
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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 Functions, Equations, and Inequalities
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 Wikipedia. "Absolute value." GNU FDL View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Absolute_valueView on Boundless.com Functions, Equations, and Inequalities
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 Boundless. "Interactive Graph: Checking Your Work." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// on Boundless.com Functions, Equations, and Inequalities
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 Boundless. "Interactive Graph: Checking Algebraic Solutions." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// View on Boundless.com Functions, Equations, and Inequalities
Free to share, print, make copies and changes. Get yours at 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
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Free to share, print, make copies and changes. Get yours at 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
Free to share, print, make copies and changes. Get yours at Boundless - LO. "Boundless." CC BY-SA BY-SA 3.0http:// 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
Attribution Connexions. "Radical Concepts -- Radical Equations." CC BY BY 3.0http://cnx.org/content/m18273/latest/ Wiktionary. "square." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/square Wiktionary. "root." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/root Wiktionary. "radical." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/radical Connexions. "Absolute Value Equations." CC BY BY 3.0http://cnx.org/content/m18201/latest/?collection=col10624 Wiktionary. "absolute value." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/absolute+value Connexions. "Rational Equations." CC BY BY 3.0http://cnx.org/content/m18302/latest/?collection=col10624 Wiktionary. "numerator." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/numerator Wiktionary. "denominator." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/denominator Boundless Learning. "Boundless." CC BY-SA BY-SA 3.0http:// Free to share, print, make copies and changes. Get yours at Functions, Equations, and Inequalities