1. Drill Lenny’s Lawncare purchased a new truck for 30x + 42 dollars. One year later the value of the truck was 12x + 28 dollars. Write an expression to represent the amount that the truck’s value decreased. Brian bought a new drill for d dollars. He paid 5% sales tax. Write an expression to represent the total amount Brian paid for the drill. At JFK live, the student ticket price is p dollars and the non- student price is $2.75 more. There were 75 student tickets sold and 34 non-student tickets sold. Write an expression to represent the total ticket sales in dollars.

2. Lesson 3.4: Solving Multi-step Equations Solving problems by working backwards Solving equations involving more than one operation

3. Working Backwards Starting at the end of the problem and undo each step Other strategies: Draw a diagram Solve a simpler (or similar) problem Make a table or chart Eliminate the possibilities Make a model Look for a pattern Guess and check Act it out Check for hidden assumptions List the possibilities Use a graph Identify the subgoals

4. Solve the following problem by working backwards Danny took some rope with him on his camping trip. He used 32 feet of rope to tie his canoe to a log on the shore. He then gave ⅓ of the remaining rope to some fellow campers who also needed to tie a canoe. The next night, he used half of the remaining rope to secure the his tent during a thunderstorm. On the last day, he used 7 feet as a fish stringer to keep the fish he had caught. After the camping trip, he had 9 feet of rope left. How much did he have at the beginning?

5. Inverse operations To undo……do thisExampleInverse operation

6. Use a table to organize StatementUndo the Statement He had 9 feet of rope left 9 feet

7. Tips for success when solving multi-step equations… “Undo” the operations in reverse of the order of operations (P, E, M/D, A/S) So, we always start with A/S first, then move on… Whatever you do to one side of the equation, you have to do to the other side. Why? It’s like a see-saw; if you add more onto one side, the see-saw will be unbalanced!

8. Solve Using Addition and Division Solve 5q – 13 = 37. Then check your solution. 5q – 13 + 13 = 37 + 13 5q = 50 5q/5 = 50/5 q = 10 Check 5(10) – 13 = 37; 50-13 = 37

9. Solving Using Subtraction and Multiplication s/12 + 6 = -1 s/12 + 6 – 6 = -1 -6 s/12 = -7 12(s/12 = -7) 12s/12 = 12(-7); s = -84 Check: -84/12 + 6 = -1; -7 + 6 = -1

10. Solving Using Multiplication and Subtraction

11. Now YOU try a few! 1. 3x + 6 = 36 2. 3 + = 6 3. 7 + 6x = -5

12. Vocabulary Consecutive integers: integers in counting order, ex: 1, 2, 3, 4… or n, n+1, n+2…. Consecutive ODD integers 1, 3, 5… n, n+2, n+4…. Consecutive EVEN integers 2, 4, 6…. n, n + 2, n + 4…. Notice that you can use the same expression to represent either odd OR even; you just need to define the value of n to be even or odd at the beginning!

13. Find three consecutive odd integers whose sum is 57 Let n = the first odd integer n+2 = the second odd integer n+4 = the third odd integer n + (n + 2) + (n + 4) = 57 3n + 6 -6 = 57 - 63n = 51 3 3 n = 17 n + 2 = 19 n + 4 = 21

14. Exit Pass Turn to page 145 in your book. Please complete the following problems on a separate piece of paper to turn in: 5-11 (odd) Homework: page 146, 22-39. Work MUST be shown.