Solving for X
 

Solving for X is a stepwise process in which you apply a fundamental rule -
    To BOTH sides of an equation, perform the opposite function of each operation in the reverse of Dear Aunt Sally.

STEP 1

     Determine order of operations

STEP 2

     Reverse order of operations

STEP 3

     For each operation -

        Determine reverse of function.

        Apply opposite function to both sides of the equation.

        Rewrite equation showing the function has cancel on one side

        Repeat until X is alone.

EXAMPLE 1

    X * 5 + 20 = 45
       ^    ^
       |     |
       1    2
The order of operations dictates that the multiplication is the first operation and the addition is the second operation.
Reverse the order of operations -

    X * 5 + 20 = 45
       ^    ^
       |     |
       2    1
We move the factors away from X by applying the opposite functions in the opposite order of Dear Aunt Sally. In this example we move the addition function first and the multiplication function second.
    X * 5 + 20 - 20 = 45 - 20 opposite of addition is subtraction

    X * 5 = 45 - 20
simplify
    X * 5 = 25
    X * 5 * 1/5 = 25 * 1/5     opposite is to multiply by inverse
    X = 25 * 1/5
simplify
    X = 5   

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