One Step Equations

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One Step Equations
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• An equation is a mathematical statement, in
  symbols, that two things are exactly the same (or
  equivalent). (LSRS)

is exactly the same as.
is exactly the same as.
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• An equation is a mathematical statement, in
  symbols, that two things are exactly the same (or
  equivalent).

is exactly the same as.
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2 2

2 2
4
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What do we use equations for?

• Equations are more than just a pile of numbers
  and letters

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Equations describe
Relationships
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What does the word relationship mean to you?
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In math, we strive to understand the mechanics of
various relationship
All major advances in technology (and society)
have arisen from the study of how things
relate.for example
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and
Gasoline
Fire
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(No Transcript)
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• Understanding the mechanics of a relationship,
  which is where we will start today, is only the
  start of any mathematical analysis.
• Communicating the results so others can
  understand is also a key aspect to the study of
  relationships. (next chapter)

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Mechanics.
x 3 4

• Some are quite simple

Some are quite complex
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The most famous equation in history only contains
3 variables, yet it dramatically changed the way
we understand the world around us.
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These kinds of relationships make up the
back-bone of mathematical study

• We shall begin with some simple operations

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To solve an equation Find the value of the
unknown that makes the equation true.

• x 7 10

x
3
Some equations can be solved by inspection.
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For other equations, a procedure is needed to
ensure accuracy

• Over the next few days we will develop and
  practice this procedure.

To solve an equation, remember the following
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1. Add / Sub and Multiply / Divide are opposite
   operations.
2. The same operation must be done on both sides of
   the equation to keep the equation true (or
   balanced).

Demonstrate with pick a number
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To isolate x, eliminate the 7
x 7 10
The opposite of add 7, is subtract 7
- 7
- 7
You must therefore impose this operation to both
sides of the equation
x
3
1
3m 12
To isolate m, eliminate the 3
The opposite of times by 3, is divide by 3
3
3
1
You must therefore impose this operation to both
sides of the equation
m
4
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1

• C -2

5 X
X 5
5
1
C
- 10
-2 y -5
2
2
y
- 3
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• See sheets
• STOP HERE

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• E mc2

E energy (J) m mass (Kg) c speed of light
3.0 X 108 m / s
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Consider a 1 liter bottle of water

• E mc2
• 1kg X (3.0 X 108)2
• 9 X 1016 Joules
• 90 000 000 000 000 000 J
• (ninety million billion)

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What is a Joule?

• Flea 7 10 J
• Free throw 15 J
• Fastball pitch 120J
• Bowl a strike 230J
• Water 9 X 1016 J
• H bomb 2.4 X 1017 J (10 bottles)
• Hurricane 3.8 X 1019 J (1000 bottles)
• Supernova 1044 J

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1 watt 1 joule expended continuously for 1
second

• 1 liter of water converted directly to energy
  could light a square filled every 10 cm with 100
  W light bulbs for 2.5 hours.
• The square would be
• 31km X 31km