Solving equations are all about focusing on what the intended goal or result is.  There are hundreds of types of equations in the mathematics world, but today’s focus will be on algebra problems, since it is essentially the basis of all mathematics.  To solve equations, first I always simply write the problem down manually on a piece of paper.  Using Excel or Word is an option, but not one that I would recommend, especially when it comes to solving in depth, larger problems you may find in the later chapters of algebra, the math may get all jumbled or out of order leading to confusion and a incorrect result. 

            So, step one write the problem down.  For this example, I will use a simple 1 variable problem just to simply demonstrate a breakdown of how I approach solving an equation.

Y – 3= 34x + 4
X= 4.  Solve for Y.

            My next step is to envision what the solution should look like.  So for this example, the goal is to isolate Y and have everything else on the other side of the equation.  There shouldn’t be a variable X in the equation once we plug in our number. 

            The next step for solving this equation is place all of our variable into the equation. 

So for our example-
 Y – 3 = 34(4) + 4

            PEMDAS is the next step to solve equations.  PEMDAS is a easy way to remember the order of operations.  The order of operations are simply: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.  Another easy way to remember this is the old trick of “Please Excuse  My Dear Aunt Sally.”  By following this order we prevent ourselves from being confused when multiple paths can be taken with a problem. 

Y-3 = 34(4) + 4
First then is the paraenthesis.
Y-3= 136 + 4

Then we will skip the exponents, since there are none in this problem, and move onto multiplication.  Again, we have none.  We go onto addition, where we can simply the right side of the equation.

Y-3 = 140

Finally, remember that what we do to one side, we must do to the other when it comes to algebra work and crossing the equal sign. 

So to move the 3 over, we must do the opposite to both sides, ADD 3.
Y- 3 +3 = 140 + 3

Simplified we get:
Y= 143

Perfect!  Our variable is on one side, and the answer is simplified fully on the right side. 

So to recap, to solve equations we want to remember our order of operations with “Please Excuse My Dear Aunt Sally,” we want to write down the problem for easy step by step access,  we want to envision our result, and finally remember to do onto both sides when crossing over the equal sign.  That’s it!  These steps to solve equations are easy to use and can really help you when it comes to solving the tricky ones later in your mathematical college career.


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