1. 3.4 Solving Multi-Step Equations Work backward is one of many problem-solving strategies that you can use. Here are some other problem-solving strategies: Draw a diagramSolve a simpler (or similar) problem Make a table or a chartEliminate possibilities Make a modelLook for a pattern Guess and checkAct it out Check for hidden assumptions List the possibilities Use a graphIdentify the subgoals

2. Work Backward to Solve a Problem Solve the following problem by working backward. After cashing her paycheck, Tara paid her father the $20 she had borrowed. She then spent half of the remaining money on a concert ticket. She bought lunch for $4.35 and had $10.55 left. What was the amount of the paycheck?

3. Work Backward to Solve a Problem The paycheck was for $49.80.

4. Solve Multi-Step Equations To solve equations with more than one operation, often called multi-step equations, undo operations by working backward.

5. Solve Using Addition and Division Solve 7m – 17 = 60. Then check your solution. 7m – 17 = 60 7m – 17 + 17 = 60 + 17 7m = 77 m = 11 Check: 7m – 17 = 60 7(11) – 17 = 60 77 – 17 = 60 60 = 60 The solution is 11.

6. Solve Multi-Step Equations See examples 3, 4, and 5.

7. Consecutive Integers Consecutive integers are integers in counting order, such as 7, 8, and 9. Beginning with an even integer and counting by two will result in consecutive even integers, such as -4, -2, 0, and 2. Beginning with an odd integer and counting by two will result in consecutive odd integers, such as -3, -1, 1, 3, and 5. The study of numbers and the relationships between them is called number theory.

8. Solve a Consecutive Integer Problem Write an equation for the problem below. Then solve the equation and answer the problem. Find three consecutive integers whose sum is -42. Let n = the least even integer. Let n + 2 = the next greater even integer, and n + 4 = the greatest of the three even integers. n + (n + 2) + (n + 4) = -42 3n + 6 = -42 3n + 6 – 6 = -42 – 6 3n = -48 n = -16 So, the three consecutive even integers are -16, -14, and -12.

9. More Practice!!!!! Homework – Worksheet 3.4.