Solving Multistep Equations
Objective
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• Write and solve multistep equations.
Solving Multistep Equations
Key Skills
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Keep it balanced!
Solve 6n + 17 = 5 + 4n
– 6n
– 6n
17 = 5 – 2n
–5 –5
12 = – 2n
÷–2
÷–2
Where
do we6nstart?
Subtract
from
The
goalofisthe
to get the
Does
it matter?
each
side
variable
onSeaside
one side
Like
driving
equal
sign.to
of the
equal
sign
and
Heights,
you
could
take
Subtract 5 from each
the numbers
on the
the side
Turnpike
to
the
of the equal
otherorside.
Parkway
Route 280
sign.
to the Parkway. Either
Divide by – 2
way gets you to the
Parkway which you
need to take to get to
n=–6
Seaside Heights.
Solving Multistep Equations
Key Skills
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Keep it balanced!
Solve 3x + 19 = 4 + 8x
– 3x
– 3x
19 = 4 + 5x
–4 –4
15 =
÷5
Subtract 3x from
Theside
goalofisthe
to get the
each
variable
equal
sign.on one side
of the equal sign and
Subtract 4 from each
the numbers on the
side of the equal
other side.
sign.
Divide by 5
5x
÷5
x=3
Solving Multistep Equations
Try This
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Keep it balanced!
Solve
– 3x – 9 = – 13 – 7x
+ 3x
+ 3x
– 9 = – 13 – 4x
+13
+13
Add 3x to each side
to get the
ofThe
the goal
equalissign.
variable on one side
of the equal sign and
Add 13 to each side
the numbers on the
of the equal sign.
other side.
Divide by – 4
4 = – 4x
÷–4
÷–4
x=–1
Solving Multistep Equations
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Solving Multistep Equations
Do this together
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Mr. Esker has to buy pencils for his company.
Supplier A charges $4 per box and $3 for
shipping. Supplier B charges $3 per box and $6
for shipping.
a. Write equations for both suppliers.
b. How many boxes would he need to buy for both
companies to charge the same amount?
Solving Multistep Equations
Do this together
Mr. Esker has to buy pencils for his company.
Supplier A charges $4 per box and $3 for
shipping. Supplier B charges $3 per box and $6
for shipping.
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E To write the equation for Supplier A, the C = $3 + 4b
B Cost (what you end up paying) is equal to
R the shipping cost (fixed amount, the
A constant where the cost starts)
+ the cost per box multiplied by how boxes are purchased.
Try writing the equation for Supplier B. C = $6 + 3b
Solving Multistep Equations
Do this together
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In order to find when the 2 Suppliers charge the same
amount, set the 2 equations equal to each other.
C = 4b + 3
C = 3b + 6
4b + 3 = 3b + 6
Now Solve for b.
Solving Multistep Equations
Do this together
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Solve 4b + 3 = 3b + 6
– 4b
– 4b
3=–b+6
–6
–6
Subtract 4b from
Theside
goalofisthe
to get
each
the variable
on one
equal
sign.
side of 6the
equal
Subtract
from
each
sign
and
the
side of the equal
numbers on the
sign.
other side.
Divide by – 1
–3=–b
÷–1
÷–1
3=b
Solving Multistep Equations
Try This
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A car leaves Newark airport and travels at a constant
rate of 65 mph to Los Angeles. The car travels through
Pittsburgh, which is 370 miles from Newark, and
through Las Vegas, which is 2500 miles from Newark.
When the car gets to Las Vegas, an airplane leaves
Pittsburgh and travels at a constant rate of 550 mph to
LA. It travels over Las Vegas as well. When will the
airplane fly over the car?
Solving Multistep Equations
Try This
Let d equal the distance traveled and h equal the elapsed
time, the distances must be equal. The important facts
are the speeds and how far each vehicle is from Newark
when the plane takes off.
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Car d = 65h + 2500
E Airplane d = 550h + 370
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550h + 370 = 65h + 2500
Solving Multistep Equations
Try This
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550h + 370 = 65h + 2500
– 370
– 370
550h = 65h + 2130
– 65h – 65h
485h = 2130
÷ 485 ÷ 485
h = 4.4 hours or
4 hours 24 minutes