Drill
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Transcript of Drill
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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.
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Lesson 3.4: Solving Multi-step Equations
Solving problems by working backwardsSolving equations involving more than one operation
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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
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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?
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Inverse operations
To undo…
…do this Example Inverse operation
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Use a table to organize
Statement Undo the StatementHe had 9 feet of rope left
9 feet
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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!
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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
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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
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Solving Using Multiplication and Subtraction
23
83
r
68r
8688 r
23
8
r
2r2
3
6
23
82
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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
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26
12
6
6
126
75677
567
x
x
x
x
x
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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!
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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
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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.