Get Away from me! - Isolating a term

Think of the equation as an onion to isolate any term that is in the center of it. Math is equitable it won't let you cheat, if you try you will FAIL! Whatever you do to one side of an equation you MUST do the exact same operation to the otherside.

As kids we learned how to count picking up our toys, then in grade one we started to add them. Grade two was not as much fun since we had to share and learned to subtract. Grade three multiplication was "taught" followed by division in grade four.

A theme appears where once we learn to do something we then learned how to undo it. In math this is seen as isolating a term. An essential use of all our learning from elementary school is applied through the rest of our math lives.

Given an equation it is not always in the form we require so we have to unwrap it into what we want. Think of the equation as an onion where each outer layer has to be removed to get to the center (required term). The outermost layer of the onion is the furthest operation to the term we are solving for.

Solve for x:

Now x is the center of the onion so first let’s determine what is the outermost layer to the innermost. Mathematically it is the reverse of Order of Operations commonly known by the acronym (PEMDAS).

In the above equation x is:

  Operation Opposite operation

                 Being squared Square root

                 Multiplied by 3 Corresponding Division

                 Added to 4t Reverse Subtraction

                 Having 2 subtracted Operation Addition

                 Finally divided by 5 Multiplication

Reading this in reverse we see that the outermost layer is division by five and the innermost is squaring.  If we perform these exact opposite operations in this order to both sides we will have isolated for x.

IMPORTANT: Whatever you do to one side you must do to the entire other side [use of brackets aid in this process].

Now we have the inner onion while preserving equity for all the other terms. No matter what math you try we often have to solve for a term that is buried deep, but this method works everytime.