Equations with the Same Equations with the Same How could you start - PDF document

Slide 1 / 79 Slide 2 / 79 Algebra I Equations 2015-08-21 www.njctl.org Slide 3 / 79 Slide 3 (Answer) / 79 Table of Contents Table of Contents Click on a topic to Click on a topic to go to that section. go to that section. · Equations with the Same Variable on Both Sides · Equations with the Same Variable on Both Sides · Solving Literal Equations · Solving Literal Equations · Substituting Values into an Equation · Substituting Values into an Equation Vocabulary Words are bolded Teacher Notes · Glossary & Standards · Glossary & Standards in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it. [This object is a pull tab] Slide 4 / 79 Slide 4 (Answer) / 79 This lesson addresses MP1, MP6 & MP7. Additional Q's to address MP standards: Math Practice Equations with the Same Equations with the Same How could you start this problem? (MP1) What operation is given in the problem? Variable on Both Sides Variable on Both Sides (MP1) What do you know about inverse operations that apply to this question? (MP7) [This object is a pull tab] Return to Table Return to Table of Contents of Contents

Slide 5 / 79 Slide 5 (Answer) / 79 Variables on Both Sides Variables on Both Sides Previously, you solved equations with variables on one side, Previously, you solved equations with variables on one side, similar to the following: similar to the following: MP6: Attend to precision. Math Practice Now, we will be given an equation with the same variable on both Now, we will be given an equation with the same variable on both Emphasize performing the inverse sides. These equations will look similar to the following: sides. These equations will look similar to the following: operation to BOTH sides of the equation. These require one additional step to get all the terms with that These require one additional step to get all the terms with that variable to one side or the other. It doesn't matter which side you variable to one side or the other. It doesn't matter which side you choose to move the variables to, but it’s typically most helpful to choose to move the variables to, but it’s typically most helpful to [This object is a pull tab] choose the side in which the coefficient of the variable will remain choose the side in which the coefficient of the variable will remain positive. positive. Slide 6 / 79 Slide 6 (Answer) / 79 Meaning of Solutions Before we encounter the new equations, let's practice how to solve an equation with the variable on only one side. Solve for x: When you have finished solving, discuss the meaning of your answer with your neighbor. Slide 7 / 79 Slide 8 / 79 Variables on Both Sides Meaning of Solutions Which side do you think would be easiest to move the variables to? Remember that you always have the ability to check your answers by substituting the value you solved for back in to the original equation. It isn't necessary to show on each problem, but is encouraged if you feel unsure about your answer.

Slide 8 (Answer) / 79 Slide 9 / 79 Variables on Both Sides Which side do you think would be easiest to move the variables to? Slide 9 (Answer) / 79 Slide 10 / 79 Example: What do you think about this equation? What is the value of x? Slide 10 (Answer) / 79 Slide 11 / 79 Example: What do you think about this equation? What is the value of x?

Slide 11 (Answer) / 79 Slide 12 / 79 1 Solve for f: Slide 12 (Answer) / 79 Slide 13 / 79 2 Solve for h: Slide 13 (Answer) / 79 Slide 14 / 79 3 Solve for x:

Slide 14 (Answer) / 79 Slide 15 / 79 No Solution Sometimes, you get an interesting answer. What do you think about this? What is the value of x? 3x - 1 = 3x + 1 -3x -3x -1 = +1 Since the equation is false, there is no solution ! No value will make this equation true. Slide 16 / 79 Slide 17 / 79 Identity 4 Solve for r: How about this one? A r = 0 What do you think about this? What is the value of x? B r = 2 3(x - 1) = 3x - 3 3x - 3 = 3x - 3 C infinitely many solutions (identity) -3x -3x -3 = -3 D no solution Since the equation is true, there are infinitely many solutions! The equation is called an identity . Any value will make this equation true. Slide 17 (Answer) / 79 Slide 18 / 79 4 Solve for r: 5 Solve for w: A w = -8 A r = 0 B w = -1 B r = 2 Answer C infinitely many solutions C infinitely many solutions (identity) C infinitely many solutions (identity) (identity) D no solution D no solution [This object is a pull tab]

Slide 18 (Answer) / 79 Slide 19 / 79 6 Solve for x: A x = 0 B x = 24 C infinitely many solutions (identity) D no solution Slide 19 (Answer) / 79 Slide 20 / 79 6 Solve for x: A x = 0 B x = 24 Answer D no solution C infinitely many solutions (identity) D no solution [This object is a pull tab] Slide 20 (Answer) / 79 Slide 21 / 79 8 In the accompanying diagram, the perimeter of ∆MNO is equal to the perimeter of square ABCD. If the sides of the triangle are represented by 4x + 4, 5x - 3, and 17, and one side of the square is represented by 3x, find the length of a side of the square. M A B 4x + 4 3x N 17 5x – 3 D C O From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

Slide 21 (Answer) / 79 Slide 22 / 79 RECAP 8 In the accompanying diagram, the perimeter of ∆MNO is equal to the perimeter of square ABCD. If the sides of the triangle are represented by 4x + 4, 5x - 3, and 17, · When solving an equation with variables on both sides, choose a and one side of the square is represented by 3x, find the side to move all of them to, then continue working to isolate the length of a side of the square. variable. Answer M A 18 B · When solving an equation where all variables are eliminated and 4x + 4 the remaining equation is false, there is No Solution. 3x 17 N · When solving an equation where all variables are eliminated and the remaining equation is true, there are Infinite Solutions. 5x – 3 D [This object is a pull tab] C O From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011. Slide 23 / 79 Slide 23 (Answer) / 79 This lesson addresses MP1, MP2, MP6 & MP7. Solving Literal Solving Literal Math Practice Additional Q's to address MP standards: How could you start this problem? (MP1) Equations Equations What operation is given in the problem? (MP1) What do you know about inverse operations that apply to this question? (MP7) [This object is a pull tab] Return to Table Return to Table of Contents of Contents Slide 24 / 79 Slide 25 / 79 Literal Equations Literal Equations Our goal is to be able to solve any equation for any variable A literal equation is an equation in which known quantities that appears in it. are expressed either wholly or in part by using letters. Let's look at a simple equation first. A good example is , which you may have seen in your physics course. Another example is which we use when studying geometry. The variables in this equation are s, d and t. In some cases, it is actually easier to work with literal equations since there are only variables and no numbers. Solving for a variable means having it alone, or isolated. This equation is currently solved for s.