Transcript Lesson 3.4: Solving Multi-step Equations

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 nonstudent 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
backwards
Solving equations involving more than
one operation

Working Backwards


Starting at the end of the problem and undo each
step
Solve a simpler (or
Draw a diagram
Other strategies:
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
He had 9 feet of rope left
Undo the Statement
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
r 8
 2
3
 3
r 8
 2
3

r 8  6
r 88  6 8
r  2
28
 2
3
6
 2
3
Now YOU try a few!
1. 3x + 6 = 36
x
2. 3 + = 6
4
3. 7 + 6x = -5
x
37 3 x63x6 56636
3 6
4x  5  7
7 37x  630
x
6 x3x31230
4 
6 x 3  123

x


6
6
4x 103 
x 42 
x  12
Vocabulary


Consecutive integers: integers in counting
order, ex: 1, 2, 3, 4… or n, n+1, n+2….
Consecutive ODD integers
Notice that you



1, 3, 5…
n, n+2, n+4….
Consecutive EVEN integers


2, 4, 6….
n, n + 2, n + 4….
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 integer
n+2 = the second odd integer
n+4 = the third odd integer
n + (n + 2) + (n + 4) = 57
3n
3n
3nn=
+
=51
617
51-6 = 57 - 6
3n + 23= 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.