ALGEBRAIC EQUATIONS

EQUATIONS AND SOLUTIONS

A correct equation is like a balance scale.

In order to determine if a given value for a variable

is a solution, you can substitute the variable with the

possible answer. If the equation is balanced or equal,

the answer is a solution.

SOLVING ADDITION EQUATIONS

GOAL: ISOLATE THE VARIABLE

Rule #: Always use the INVERSE operation.

Rule #2: Whatever you do to the left side you must

do to the right side or they are no longer balanced.

SOLVING

To get the variable by itself, take away or subtract

the number that was added to the variable.

Remember the rule! Because you subtract the

number from the side with the variable, you must

also subtract the same number from the side without

the variable.

SOLVING SUBTRACTION EQUATIONS

GOAL: ISOLATE THE VARIABLE

Rule #: Always use the INVERSE operation.

Rule #2: Whatever you do to the left side you must

do to the right side or they are no longer balanced.

SOLVING

To get the variable by itself, add the number that

was subtracted to the variable.

Remember the rule! Because you add the number

to the side with the variable, you must also add the

same number from the side without the variable.

SOLVING MULTIPLICATION EQUATIONS

GOAL: ISOLATE THE VARIABLE

Rule #: Always use the INVERSE operation.

Rule #2: Whatever you do to the left side you must

do to the right side or they are no longer balanced.

SOLVING

To get the variable by itself, divide the number that

was multiplied to the variable.

Remember the rule! Because you divide the

number on the side with the variable, you must also

divide the same number from the side without the

variable.

SOLVING DIVISION EQUATIONS

GOAL: ISOLATE THE VARIABLE

Rule #: Always use the INVERSE operation.

Rule #2: Whatever you do to the left side you must

do to the right side or they are no longer balanced.

SOLVING

To get the variable by itself, multiply the number

that is the divisor.

Remember the rule! Because you multiply the

number on the side with the variable, you must also

multiply by the same number on the side without the

variable.

GOAL: ISOLATE THE

VARIABLE

Rule 1: Always use the

inverse operation.

Rule 2: Whatever you do

to the left side you must

do to the right side or

they are no longer

balanced.

Fill in on pages 8

AND 9!

SOLVING:

1. Combine all like terms, if

necessary.

2. If there are variables on

both sides, get the variables

on one side by using the

opposite operation to get

rid of the variable with the

smallest coefficient.

3. Use opposite or inverse

operations to get rid of the

numbers on the same side

as the variable.

4. Don’t forget – Whatever you

do to one side, you must do

the other.

DECIMALS- PAGE 8

7.4 + y = 18.

2

-7.4 - 7.4

y=

10.8

2.3z= 9.2

2.3 2.3

z= 4

FRACTIONS- PAGE 9

h + 3/8 = 5/8

- 3/8 -3/8

h = 2/8 (1/4)

1/2n=3/8

1/2 1/2

n= 6/8 (3/4)