Solving One-Step Equations Gangnam Style
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Transcript Solving One-Step Equations Gangnam Style
Solving One-Step
Equations
Gangnam Style
Video
Step-by-step
Vocabulary
Inverse Operationtwo operations that “undo” each other,
such as addition and subtraction
Equivalent Equationsequations that have the same solution
Solving an equation using subtraction
Solve m + 12 = 7
First write the original equation.
m + 12 = 7
Solving an equation using subtraction
Solve m + 12 = 7
First write the original equation.
m + 12 = 7
Then do the inverse operation.
Subtract 12 from each side.
m + 12 = 7
- 12 -12
Solving an equation using subtraction
Solve m + 12 = 7
First write the original equation.
m + 12 = 7
Then do the inverse operation.
Subtract 12 from each side.
m + 12 = 7
- 12 -12
Simplify
m=
-5
Check your solution.
m + 12 = 7
Check your solution.
m + 12 = 7
-5 + 12 =? 7 Substitute the solution for the
variable
Check your solution.
m + 12 = 7
-5 + 12 =? 7
7 = 7
Simplify
Check your solution.
m + 12 = 7
-5 + 12 =? 7
7 = 7
YES!
SOLUTION CONFIRMED!
Solving an equation using addition
Solve -2 = x - 9
Solving an equation using addition
Solve -2 = x - 9
First write the original equation.
Solving an equation using subtraction
Solve -2 = x - 9
First write the original equation.
-2 = x - 9
Then do the inverse operation.
Which is what?
Solving an equation using subtraction
Solve -2 = x - 9
First write the original equation.
-2 = x - 9
Then do the inverse operation.
Add 9 to each side.
-2 = x – 9
+9
+9
Solving an equation using subtraction
Solve -2 = x - 9
First write the original equation.
-2 = x - 9
Then do the inverse operation.
Add 9 to each side.
-2 = x – 9
+9
+9
Simplify
+7=x
Check your solution.
-2 = x - 9
-2 =? 7 – 9
-2 = -2
YES!
SOLUTION CONFIRMED!
Writing and Solving an Equation
You are traveling to Louisville, Kentucky.
You have already traveled 122 miles, and
you just passed a road sign that said
Louisville is 76 miles away. How far is
Louisville from the start of your trip?
Writing and Solving an Equation
Let d represent the distance from the start
of your trip to Louisville.
Write a verbal model.
Distance from the
- Distance traveled = Remaining distance
start to Louisville
Writing and Solving an Equation
Let d represent the distance from the start
of your trip to Louisville.
Write a verbal model.
Distance from the
- Distance traveled = Remaining distance
start to Louisville
Use the verbal model to write an equation.
d
- 122
= 76
Writing and Solving an Equation
Let d represent the distance from the start of your
trip to Louisville.
Write a verbal model.
Distance from the
- Distance traveled = Remaining distance
start to Louisville
Use the verbal model to write an equation.
d
- 122
= 76
Inverse operation
+ 122
+ 122
Writing and Solving an Equation
Let d represent the distance from the start of your trip to
Louisville.
Write a verbal model.
- Distance traveled
= Remaining distance
Distance from the
start to Louisville
Use the verbal model to write an equation.
d
- 122
= 76
Inverse operation
+ 122
+ 122
Simplify
d
= 198
Check your solution
d = 198
d – 122 = 76
198 – 122 =? 76
76
= 76
YES!
Louisville is 198 miles from the start of your trip.
Your turn-Shopping Spree
You have $37 left after shopping. You
started with $85. How much money did you
spend?
Write a verbal model, equation, and then
solve.
Shopping Spree
Money + Money
left
spent
= Money
started
Let m be the money I spent.
Shopping Spree
Money + Money
left
spent
=
Money
started
Let m be the money I spent.
37
+
m
= 85
Shopping Spree
Money + Money
left
spent
=
Money
started
Let m be the money I spent.
37
+
m
= 85
-37
- 37
Shopping Spree
Money
left
+ Money
spent
=
Money
started
Let m be the money I spent.
37
+
m
= 85
-37
- 37
m
= 48
Check your Solution
37 + m = 85
37 + 48 =? 85
85 =
YES!
85
One more-Bike Race
You are in a 50 km bike race. You have to
bike 21 kilometers until you reach the finish
line. How far have you already biked?
Bike Race
Total
=
distance
Distance
traveled
d = distance traveled
+
Distance
left
Bike Race
50 = d + 21
- 21
- 21
29 = d
Check
50 = d + 21
50 =? 29 + 21
50 = 50
YES!
Equations-Multiplying & Dividing
Gangnam Style
Video
Solving an Equation Using Division
Solve 9x = -108
Solving an Equation Using Division
Solve 9x = -108
Inverse Operation?
Solving an Equation Using Division
Solve 9x = -108
Inverse Operation?
Divide by 9
Solving an Equation Using Division
Solve 9x = -108
Inverse Operation?
Divide by 9
9x = -108
9
9
Solving an Equation Using Division
Solve 9x = -108
Inverse Operation?
Divide by 9
9x = -108
9
9
x = -12
Check
9x = -108
9 (-12) =? -108
-108 = -108
YES!
Solving an Equation Using
Multiplication
k =5
25
Solving an Equation Using
Multiplication
k =5
25
Inverse Operation?
Solving an Equation Using
Multiplication
k =5
25
25
k =5
25
25
Solving an Equation Using
Multiplication
k =5
25
25
k =5
25
25
k = 125
Check
k =5
25
125 =? 5
25
5 = 5
YES!
Writing and Solving an Equation
If you divide your camera film equally over
your 7-day vacation, you will take 25
pictures a day. How many exposures do
you have?
Let e represent the number of exposures.
Writing and Solving an Equation
Total number =
Number of days
# of pics taken
Writing and Solving an Equation
Total number =
Number of days
e
7
=
25
# of pics taken
Writing and Solving an Equation
Total number =
Number of days
7 e
7
=
25
# of pics taken
7
Writing and Solving an Equation
Total number =
Number of days
7 e
7
e
=
25
=
175
# of pics taken
7
Check
e
7
=
175 =?
7
25
25
Check
e
=
7
175 =?
7
25 =
25
25
25
You have 175 exposures.
Your turn
Your parents divide money evenly among
you and your three siblings. Each of you
receives $75. Find the total amount your
parents gave.
Let s equal the total amount of money your
parents gave.
s = 75
4
4 s = 75
4
4
4 s = 75
4
s = 300
4
Check
s = 75
4
300 =? 75
4
Check
s = 75
4
300 =? 75
4
75 = 75!
One more
You purchased 9 yards of fabric. The total
cost is $45. Find the cost per yard of the
fabric.
Let f equal the cost per yard of fabric.
9f = 45
9f = 45
9
9
9f = 45
9
9
f
= 5
Check
9f = 45
9 (5) =? 45
Check
9f = 45
9 (5) =? 45
45
= 45!
Gangnam Style