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ONE STEP EQUATIONS ONE STEP EQUATIONS An equation is like a balance scale because it shows that two quantities are equal. What you do to one side of the equation must also be done to the other side to keep it balanced. ONE STEP EQUATIONS To solve one step equations, you need to ask three questions about the equation: • What is the variable? • What operation is performed on the variable? • What is the inverse operation? (The one that will undo what is being done to the variable) ONE STEP EQUATIONS Example 1 Solve x + 4 = 12 What is the variable? The variable is x. What operation is being performed on the variable? Addition. What is the inverse operation (the one that will undo what is being done to the variable)? Subtraction. Using the subtraction property of equality, subtract 4 from both sides of the equation. The subtraction property of equality tells us to subtract the same thing on both sides to keep the equation equal. x + 4 = 12 -4 -4 x = 8 ONE STEP EQUATIONS Example 2 Solve y - 7 = -13 What is the variable? The variable is y. What operation is being performed on the variable? Subtraction. What is the inverse operation (the one that will undo what is being done to the variable)? Addition. Using the addition property of equality, add 7 to both sides of the equation. The addition property of equality tells us to add the same thing on both sides to keep the equation equal. y - 7 = -13 +7 +7 y = -6 ONE STEP EQUATIONS Example 3 Solve –6a = 12 What is the variable? The variable is a. What operation is being performed on the variable? Multiplication. What is the inverse operation (the one that will undo what is being done to the variable)? Division Using the division property of equality, divide both sides of the equation by –6. The division property of equality tells us to divide the same thing on both sides to keep the equation equal. –6a = 12 -6 -6 a = -2 ONE STEP EQUATIONS Example 4 Solve b = -10 What is the variable? 2 The variable is b. What operation is being performed on the variable? Division. What is the inverse operation (the one that will undo what is being done to the variable)? Multiplication Using the multiplication property of equality, multiply both sides of the equation by 2. The multiplication property of equality tells us to multiply the same thing on both sides to keep the equation equal. b = -10 2 b 2 • = -10 • 2 2 b = -20 Your Turn: Solve the following equations with one step (show your work!!): 1. r + 4 = 17 2. g - 15 = -11 3. 13 + p = - 9 4. -5b = 85 5. - 7v = - 91 6. w = -2 3 Answers: 1. r = 13 2. g = 4 3. p = - 22 4. b = - 17 5. v = 13 6. w=-6 Word Problems with One Step Equations You will need to know how to solve word problems involving these equations, by using the four-step problem solving plan: 1. Read/Explore the problem 2. Plan the solution 3. Solve the problem 4. Examine the solution 1. Explore the problem First, read the problem carefully, then: • Identify what information is given • Identify what you are asked to find 2. Plan the Solution • Choose a variable to represent the unknown that you are trying to solve for • Create an algebraic equation for solving 3. Solve the Problem 4. Examine the Solution • use algebraic methods • Is your answer “reasonable” ? • Show your work! • Did you check your work to be sure? Try it ! Write an Equation and Solve the Problem: Noah received a paycheck on Friday. After buying some athletic shoes for $112, he had $96 left. How much was his paycheck? • Let p = paycheck • p - 112 = 96 • + 112 +112 • p = 208 • Noah’s paycheck was $208.

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posted: | 10/3/2012 |

language: | simple |

pages: | 15 |

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