Simplifying Algebraic Expressions Click here to find out how!here

Solving Equations Finding the value of a variable

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.

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 by isolating 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

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

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

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

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

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 - a number is added to x.

Here are the 5 basic kinds of problems. Problem type 1 the opposite of addition is subtraction

Here are the 5 basic kinds of problems. Problem type 1

Here are the 5 basic kinds of problems. Problem type 2 - a number is subtracted from x

Here are the 5 basic kinds of problems. Problem type 2 the opposite of subtraction is addition

Here are the 5 basic kinds of problems. Problem type 2

Here are the 5 basic kinds of problems. Problem type 3 - x is multiplied by a number

Here are the 5 basic kinds of problems. Problem type 3 the opposite of multiplication is division

Here are the 5 basic kinds of problems. Problem type 3

Here are the 5 basic kinds of problems. Problem type 4 - x is divided by a number

Here are the 5 basic kinds of problems. Problem type 4 the opposite of division is multiplication

Here are the 5 basic kinds of problems. Problem type 4

Here are the 5 basic kinds of problems. Problem type 5 - a fraction is multiplied by x

Here are the 5 basic kinds of problems. Problem type 5 any number times it’s reciprocal is “1”

Here are the 5 basic kinds of problems. Problem type 5

Here are the 5 basic kinds of problems. Problem type 5

Solving Proportions

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.

Two step problems (two basic problems in one)

Solving two-step Proportions

Equations with variables on both sides of the equation.

Java applets to practice more. Algebra Balance Scales Algebra Balance Scales - Negatives