 # ONE STEP EQUATIONS What you do to one side of the equation must also be done to the other side to keep it balanced. An equation is like a balance scale.

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ONE STEP EQUATIONS

What you do to one side of the equation must also be done to the other side to keep it balanced. An equation is like a balance scale because it shows that two quantities are equal.

ONE STEP EQUATIONS What is the variable? To solve one step equations, you need to ask three questions about the equation: 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? Using the subtraction property of equality, subtract 4 from both sides of the equation. - 4 x x + 4 = 12 The variable is x. Addition. Subtraction. What is the inverse operation (the one that will undo what is being done to the variable)? What operation is being performed on the variable? - 4 8= The subtraction property of equality tells us to subtract the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONS Example 2 Solve y - 7 = -13 What is the variable? Using the addition property of equality, add 7 to both sides of the equation. y - 7 = -13 + 7 y The variable is y. Subtraction. Addition. What operation is being performed on the variable? What is the inverse operation (the one that will undo what is being done to the variable)? + 7 =-6 The addition property of equality tells us to add the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONS Example 3 Solve –6a = 12 What is the variable? Using the division property of equality, divide both sides of the equation by –6. –6a = 12 -6 a 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 -6 =-2 The division property of equality tells us to divide the same thing on both sides to keep the equation equal.

ONE STEP EQUATIONS Example 4 Solve What is the variable? Using the multiplication property of equality, multiply both sides of the equation by 2. = -10 b 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 = -102 2 =-20 =-10 The multiplication property of equality tells us to multiply the same thing on both sides to keep the equation equal.

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

Step 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.S olve the Problem use algebraic methods Show your work! 4.E xamine the Solution Is your answer reasonable ? 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 Noahs paycheck was \$208.

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