Drill
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Transcript of 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
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x
x
x
26
12
6
6
126
75677
567
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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.