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Solving Multi-Step Equations
Use the Order of Operations Backwards
Solving Equations that Contain Like Terms
11b+4-6b+2=26
15d-6+9d+8=50
Solving Word Problems
First write an equation for the problem,
and then solve
Tyler rents a car. It costs $300, plus
$50 dollars per day. His total bill was
$500. How many days did he have the car?
300 + 50d = 500
Equations with variables on both sides
Justifying Steps For Solving Equations
When solving equations, it
is important to know why each operation works
3x + 4 = 16
- 4 -4 Subtraction Property of Equality
3x + 0 = 12 Additive inverse (left side) and simplify (right side)
3x = 12 Additive Identity
÷3 ÷3 Division Property of Equality
1x = 4 Multiplicative inverse (left side) and simplify (right side)
x = 4 Multiplicative identity
Elena is renting an apartment. She pays
a security deposit of $300 and here rent is
$600 a month. After how many months
will she have spent $2700?
The temperature for a week in December
starts at 30 degrees and drops 3 degrees
every day. After how many days will the
temperature be 18 degrees?
Ian's age is equal to twice his grandma's
age, divided by ten. If Ian is 12, how old
is his grandma?
Ryan and Ruth go to the carnival. They
each start out with $30. It costs them 2
dollars for each ride they go on. If they
each have $14 at the end of the day, how
many rides did they go on?
Jason and Alex are baking cookies. It takes
them 20 minutes to make the dough and 10
minutes to bake each batch of cookies. If
they bake for 90 minutes, how many
batches of cookies can they make?
Adam and Alec's rent a car to go on a trip.
The car costs $200, plus $.50 for evey mile
they drive. If they spend $350, how many
miles did they drive?
Maddie, Emily, Emma and Caroline go on
a trip. They split the cost of the motel 4
ways and each one of the girls brings along
$100 in spending money. If each girl spent
$175, how much did the motel cost?
6h - 3 + 2h = 45 - 2h + 2
11-2
3(2c - 4) = 2(26 - c)
15 - 7v = 5v - 71
2x - 7 = 3 - 3x
1. Get all of the variables on
one side
+3x
4x+4+2x-7=27
5x - 7 = 3
2. Solve
+7
7g + 2 = 3g + 14
First, combine like terms
6x-3=27
5x = 10
__
5
Add 3 to both sides
+3
x = 2
6x=30
_
6
Divide both sides by 6.
x=5
9n + 3 - 4n = 2n + 45 - 6
k = 1
6(k + 4) = 3(3k + 7)
6f +3 = 21
-3
First subtract 3 from both sides
6f = 18
Next, divide both sides by 2
__
3
f = 6
k
__
+ 9 = 2
3
5y - 4 = 26
15 + 9r = 105
v
__
- 9 = -1
8
_
1
2
x - 3 = 15
12x + 4 = 40
2(x + 6) = 32
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