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.