Simplifying Algebraic Expressions

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Simplifying Algebraic Expressions
Click here to find out how!
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Solving Equations

• Finding the value of a variable

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Solving Equations

• An equation is two expressions separated by an
  equal sign. Equations work similar to a balance,
  where the stand is the equal sign and the trays
  contain the expressions. In order to keep the
  trays balanced, you must add, subtract, multiply
  or divide the same amount to both trays in order
  to keep it balanced.

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So the next question is what are we supposed to
do mathematically to both sides of an equation?
The object of solving equations is to find the
VALUE of the variable contained in the equation.
Keep in mind this goal - Finding the value of a
variable can be accomplished byisolating one,
positive, variable on one side of the equation.
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How do you isolate one, positive variable?
In Algebra, we use Properties of Equality to
help us to isolate and create one, positive
variable.
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Properties of Equality allow us to create zero or
create one whenever needed.
This is necessary in order to reach our goal -
to isolate one, positive variable.
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There are five basic ways that numbers affect
variables.
1) They can be added to the variable
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There are five basic ways that numbers affect
variables.
1) They can be added to the variable

1. They can be subtracted from the
   variable

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There are five basic ways that numbers affect
variables.
1) They can be added to the variable

1. They can be subtracted from the
   variable

3) They can be multiplied by a variable
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There are five basic ways that numbers affect
variables.
1) They can be added to the variable

1. They can be subtracted from the
   variable

3) They can be multiplied by a variable
4) The variable can be divided by a number
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There are five basic ways that numbers affect
variables.
1) They can be added to the variable

1. They can be subtracted from the
   variable

3) They can be multiplied by a variable
4) The variable can be divided by a number
5) The variable can be multiplied by a fraction
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Tools that you will use to aide you in isolating
and creating one, positive variable are called
properties of equality. When using these
properties they always apply to both sides of the
equation. This is why they work. They always
keep an equation balanced.
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A number added to a variable can dissapear by
adding its opposite.Addition/Subtraction
Property of Equality
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A number added to a variable can dissapear by
adding its opposite.Addition/Subtraction
Property of Equality A number multiplied by a
variable can be changed to 1 by dividing the
number by itself.Division Property of Equality
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A number added to a variable can dissapear by
adding its opposite.Addition/Subtraction
Property of Equality A number multiplied by a
variable can be changed to 1 by dividing the
number by itself.Division Property of Equality
A number divided by a variable can be changed
to 1 by multiplying the number by itself.
Multiplication Property of Equality
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A number added to a variable can dissapear by
adding its opposite.Addition/Subtraction
Property of Equality A number multiplied by a
variable can be changed to 1 by dividing the
number by itself.Division Property of Equality
A number divided by a variable can be changed
to 1 by multiplying the number by itself.
Multiplication Property of EqualityAny
fraction times its reciprocal is 1.Property of
Recipricols
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Here are the 5 basic kinds of problems.
Problem type 1 - a number is added to x.
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Here are the 5 basic kinds of problems.
Problem type 1
the opposite of addition is subtraction
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Here are the 5 basic kinds of problems.
Problem type 1
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Here are the 5 basic kinds of problems.
Problem type 2 - a number is subtracted
from x
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Here are the 5 basic kinds of problems.
Problem type 2
the opposite of subtraction is addition
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Here are the 5 basic kinds of problems.
Problem type 2
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Here are the 5 basic kinds of problems.
Problem type 3 - x is multiplied by a number
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Here are the 5 basic kinds of problems.
Problem type 3
the opposite of multiplication is division
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Here are the 5 basic kinds of problems.
Problem type 3
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Here are the 5 basic kinds of problems.
Problem type 4 - x is divided by a number
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Here are the 5 basic kinds of problems.
Problem type 4
the opposite of division is multiplication
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Here are the 5 basic kinds of problems.
Problem type 4
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Here are the 5 basic kinds of problems.
Problem type 5 - a fraction is multiplied by x
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Here are the 5 basic kinds of problems.
Problem type 5
any number times its reciprocal is 1
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Here are the 5 basic kinds of problems.
Problem type 5
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Here are the 5 basic kinds of problems.
Problem type 5
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Solving Proportions
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Solving Proportions
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Solving Proportions
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Solving Proportions
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Solving Proportions
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Two step problems(two basic problems in one)
Simplify anything that can be simplified. ? Any
like terms on the same side of the equal
sign? ? Any multiplication or
distributive property to do? Get rid of anything
that is added or subtracted to the
variable. Create 1 positive variable.
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Two step problems(two basic problems in one)
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Solving two-step Proportions
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Solving two-step Proportions
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Solving two-step Proportions
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Solving two-step Proportions
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Solving two-step Proportions
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Solving two-step Proportions
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Solving two-step Proportions
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Equations with variables on both sides of the
equation.
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Equations with variables on both sides of the
equation.
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Equations with variables on both sides of the
equation.
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Equations with variables on both sides of the
equation.
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Equations with variables on both sides of the
equation.
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Equations with variables on both sides of the
equation.
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Equations with variables on both sides of the
equation.
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Java applets to practice more.

• Algebra Balance Scales
• Algebra Balance Scales - Negatives