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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