Drill

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.

Lesson 3.4: Solving Multi-step Equations

Solving problems by working backwardsSolving equations involving more than one operation

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

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?

Inverse operations

To undo…

…do this Example Inverse operation

Use a table to organize

Statement Undo the StatementHe had 9 feet of rope left

9 feet

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!

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

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

Solving Using Multiplication and Subtraction

23

83

r

68r

8688 r

23

8

r

2r2

3

6

23

82

Now YOU try a few!

1. 3x + 6 = 36

2. 3 + = 6

3. 7 + 6x = -5

103

30

3

3

303

636663

x

x

x

x

4

x

12

34

4

34

364

33

x

x

x

x

26

12

6

6

126

75677

567

x

x

x

x

x

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!

Find three consecutive odd integers whose sum is 57

Let n = the first odd integern+2 = the second odd integern+4 = the third odd integern + (n + 2) + (n + 4) = 57

3n + 6 -6 = 57 - 63n = 513n = 51 3 3

n = 17

n + 2 = 19

n + 4 = 21

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.