Simplifying Algebraic Expressions
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Solving EquationsAn 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.
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 valueof a variable can be accomplished byisolating one, positive, variable on
one side of the equation.
How do you isolate one, positive variable?
In Algebra, we use Properties of Equality to help us to isolate and create one, positive variable.
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.
There are five basic ways that numbers affect variables.
1) They can be added to the variable
2) They can be subtracted from the variable
x 23
There are five basic ways that numbers affect variables.
1) They can be added to the variable
2) They can be subtracted from the variable
3) They can be multiplied by a variable
3x
There are five basic ways that numbers affect variables.
1) They can be added to the variable
2) They can be subtracted from the variable
3) They can be multiplied by a variable
4) The variable can be divided by a number x
5
There are five basic ways that numbers affect variables.
1) They can be added to the variable
2) 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
34x
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.
A number added to a variable can dissapear by adding it’s opposite.
Addition/Subtraction Property of Equality
A number added to a variable can dissapear by adding it’s 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 added to a variable can dissapear by adding it’s 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
A number added to a variable can dissapear by adding it’s 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
Any fraction times it’s reciprocal is 1.Property of Recipricols
Here are the 5 basic kinds of problems.
Problem type 1
x 12 4 12 12
the opposite of addition issubtraction
Here are the 5 basic kinds of problems.
Problem type 2
x 6 9
6 6
the opposite ofsubtraction is addition
Here are the 5 basic kinds of problems.
Problem type 3 12x 36
12x 12
36 12
the opposite of multiplication is division
Here are the 5 basic kinds of problems.
Problem type 4x 7
3
71
x 7
3 7 the opposite of division is multiplication
Here are the 5 basic kinds of problems.
Problem type 5
23x 12
32
23x
121
32
any number times it’s reciprocal is“1”
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.
Equations with variables on both sides of the equation.
2x 5 6x 25
6x 6x
4x 5 25
5 5
4x 20
4x4
204
x 5
Equations with variables on both sides of the equation.
2x 5 6x 25
6x 6x
4x 5 25
5 5
4x 20
4x4
204
x 5
Equations with variables on both sides of the equation.
2x 5 6x 25
6x 6x
4x 5 25
5 5
4x 20
4x4
204
x 5
Equations with variables on both sides of the equation.
2x 5 6x 25
6x 6x
4x 5 25
5 5
4x 20
4x4
204
x 5
Equations with variables on both sides of the equation.
2x 5 6x 25
6x 6x
4x 5 25
5 5
4x 20
4x4
204
x 5
Equations with variables on both sides of the equation.
2x 5 6x 25
6x 6x
4x 5 25
5 5
4x 20
4x4
204
x 5
Equations with variables on both sides of the equation.
2x 5 6x 25
6x 6x
4x 5 25
5 5
4x 20
4x4
204
x 5
Java applets to practice more.
•Algebra Balance Scales
•Algebra Balance Scales - Negatives