Drill

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:

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 multiplication by an integer division by an integer /5 X 5 division by an integer multiplication by an integer /5 X 5 multiplication by an fraction multiplication by its reciprocal X 1/4 X 4/1 addition subtraction + 6 - 6 subtraction addition - 6 + 6

6. Use a table to organize He used 7 feet as a fish stringer 9 feet + 7 feet = 16 feet He used half of the remaining rope to secure the tent 16 feet X 2 = 32 feet He gave 1/3 of the rope to fellow campers 32 feet X 3/2= 48 feet which means he kept 2/3 of the rope He used 32 feet of rope to tie his canoe 48 feet + 32 feet = 80 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 add 13 to both sides simplify divide both sides by 5 simplify

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 subtract 6 from both sides simplify multiply each side by 12 simplify

10. Solving Using Multiplication and Subtraction Check please! Multiply both sides by -3 Subtract 8 from both sides simplify simplify

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 = 51 3n + 6 -6 = 57 - 6 3n = 51 3 3 n = 17 n + 2 = 19 n + 4 = 21 3n + 6 = 57

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.