1.5 One Step Equations Intro, Notes, and Practice.
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Transcript of 1.5 One Step Equations Intro, Notes, and Practice.
1.5 One Step EquationsIntro, Notes, and Practice
How do inverse operations help you solve one-step equations?
Essential Question
The Great Lakes
The amount of water in Lake Superior is 1720 cubic miles more than the amount of water in Lake Michigan. Lake Huron has 330 cubic miles of water less than Lake Michigan. If the total amount of water in the three lakes is 4,930 cubic miles, how much water is in Lakes Huron, Michigan, and Superior.
The Great Lakes
Describe/ Draw:Lake Michigan: Lake Superior:Lake Huron:
The amount of water in Lake Superior is 1720 cubic miles more than the amount of water in Lake Michigan. Lake Huron has 330
cubic miles of water less than Lake Michigan. If the total amount of water in the three lakes is 4,930 cubic miles, how much water is in
Lakes Huron, Michigan, and Superior.
LM1720 more than LM330 less than LM
Do: M + S + H
Decide:
M + S + H = 4,930
The amount of water in Lake Superior is 1720 cubic miles more than the amount of water in Lake Michigan. Lake Huron has 330
cubic miles of water less than Lake Michigan. If the total amount of water in the three lakes is 4,930 cubic miles, how much water is in
Lakes Huron, Michigan, and Superior.
Define: M S H M + S + H 4930x 1720
more330 less
1000
2720
670 1000 + 2720 + 670 = 4390
Too small200
03720
1670
2000 + 3720 + 1670 = 7390
Too big
This could take a while.
If only there was an easier way…
The amount of water in Lake Superior is 1720 cubic miles more than the amount of water in Lake Michigan. Lake Huron has 330 cubic miles of
water less than Lake Michigan. If the total amount of water in the three
lakes is 4,930 cubic miles, how much water is in Lakes Huron, Michigan, and
Superior.
Define: M S H M + S + H 4930x x +
1720x - 330
Solve Using an Equation
Describe/ Draw:Lake Michigan: Lake Superior:Lake Huron:
xx + 1720x - 330
x + x + 1720 + x – 330 = 4930
The amount of water in Lake Superior is 1720 cubic miles more than the amount of water in Lake Michigan. Lake Huron has 330 cubic miles of
water less than Lake Michigan. If the total amount of water in the three
lakes is 4,930 cubic miles, how much water is in Lakes Huron, Michigan, and
Superior.
Solve Using an Equation
Describe/ Draw:Lake Michigan: Lake Superior:Lake Huron:
xx + 1720x - 330
x + x + 1720 + x – 330 = 4930
Combine Like Terms
3x + 1390 = 4930
Zero pair (goodbye friends)
- 1390 - 1390 3x = 3540
Divide (goodbye family) 3 3
x = 1180Lake Michigan has 1180
cubic miles.
The amount of water in Lake Superior is 1720 cubic miles more than the amount of water in Lake Michigan. Lake Huron has 330 cubic miles of water less than Lake Michigan. If the total amount of water in the three lakes is 4,930 cubic
miles, how much water is in Lakes Huron, Michigan, and Superior.
What about the others?
Describe/ Draw:Lake Michigan: Lake Superior:
Lake Huron:
x
x + 1720
x - 330
= 1180
Lake Michigan has 1180 cubic miles.= 1180 + 1720 = 2900Lake Superior has 2900
cubic miles.= 1180 – 330 = 850Lake Huron has 850 cubic
miles.
Hello, Equations! Guess and Check is a helpful process, but it
becomes way too difficult as math gets more complex.
We are going to increase our confidence in using equations to solve problems by starting off with simpler problems and building up our skills.
Some problems may seem easy enough to logically figure out the answer without using an equation, but don’t be tempted! You need to practice on the easier problems so that you can better tackle more complex problems!
Goodbye, Guess and Check
Vocabulary:
Operation: something that is done to a value Such as: addition, subtraction, multiplication,
division
Inverse: opposite/reverse; an operation that undoes an action Addition Subtraction Multiplication Division
Solving One Step Equations
Steps:
Locate the variable and identify what operation is being done to it
Do the inverse operation Be sure to stay balanced and fair by doing
the exact same thing to both sides Plug your answer back into the original
equation to check your solution
Solving One Step Equations
n – 19 = -41 + 19 + 19 n = -22
Examples
Check: (-22) – 19 = -41 -41 = -41
= 8 n = 12
∙32
32∙
81∙32=?
Check:(12) = 8 8 = 8
1) r + 12 = -8 2)
3) = 4) -12a = -168
When you are finished, complete the following problems in your textbook:
Page 110 #1 – 7, Page 115 #1 – 3 and 7 – 9 ,
and Page 117 #19 – 29
*Check answers to odd problems in back of textbook
Practice
-20 -36
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