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## Solving one step equations

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**Properties of Equality**• Addition: If a = b then a + c = b + c. 2. Subtraction: If a = b then a – c = b– c. 3. Multiplication: If a = b then ac = bc. 4. Division: If a = b and c ≠ 0 then a/c = b/c**Rules to Remember**Quick Facts and Definitions: • When solving an equation, the goal is to get the variable by itself on one side of the equation. • Addition and subtraction are inverse operations. (opposites) • Multiplication and division are inverse operations. (opposites)**Solving Equations Requires BALANCE!**Your equals sign will be the fulcrum (balancing point)! Just remember, whatever you do to one side must be done to the other side to maintain balance……..**Addition / Subtraction**• If the number to move is positive, subtract it from both sides of the equation. • If the number to move is negative, add its positive value to both sides of the equation.**Solving with Addition**Solve the following equation for x: x – 4 = 9 + 4+4 x = 13 We are able to get the x by itself by ADDING 4 to each side! (you WILL show this step in your homework!!)**Solving with Subtraction**Solve the following equation for p: p + 7 = 21 - 7- 7 p = 14 We are able to get the p by itself by SUBTRACTING 7 from each side! (you WILL show this step in your homework!!)**Solving with Division**Solve the following equation for m: 3 m = 18 • Divide both sides by 3 and simplify -- your work should look like this : • 3 m = 18 3 3 • m = 6 (you WILL show this step in your homework!!)**Solving with Multiplication**Problems involving fractions are solved using multiplication, and the knowledge of multiplicative inverses (reciprocals)**Example :**Solve the following equation for n: 2n = 3 5 7 • Multiply each side by the inverse of 25 : • 5•2n = 3•5 2 5 7 2 • n = 15 14**Your Turn:**Solve the following equations with one step (show your work!!): • r + 4 = 17 • g - 15 = -11 • 13 + p = - 9 • -5b = 85 • - 7v = - 91 • w = -2 3 9**Answers:**• r = 13 • g = 4 • p = - 22 • b = - 17 • v = 13 • w = - 2/3**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: • Explore the problem • Plan the solution • Solve the problem • 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**Solve the Problem**use algebraic methods Show your work! Examine the Solution Is your answer “reasonable” ? Did you check your work to be sure?**Let’s try it!**Read the following: One mile is equal to approximately 1.6 kilometers. A local running club is holding a 10 kilometer race. What is the length of the race in miles? • Define aVariable Let m = the number of miles • 1.6 • m = 10 • Divide both sides by 1.6 (calculators ok) • m = 6.25 • The length of the race is 6.25 miles.**One more !**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.