How do you know which operation to preform first when solving an equation

Question

need help with my homework 

 

Answer 1

Hi Jose.

 

Remember the goal is to "isolate" the variable you are solving the equation for.

 

You have heard PEMDAS (we use the sentence "Please Excuse My Dear Aunt Sally to remember the ORDER OF OPERATIONS).

 

When you are SIMPLIFYING, you go in the PEMDAS order, but when you are SOLVING, you are "undo-ing" a simplified expression, so you do PEMDAS BACKWARDS in order to isolate the variable.

 

For example.

If the equation is  

 

4x-3 = 5

 

PEMDAS backwards would mean to do any adding or subtracting first with the goal of isolating x.  This gets the 4x alone on the left.

 

4x - 3 = 5

     +3       +3

 

4x = 8

 

The next backwards PEMDAS is multiplication and division, so we divide both sides by 4 and that gets x alone and we have our solution.

 

 

4x = 8

--      --

4      4

 

x = 2

 

So if you keep in mind that you will do P E (MD) (AS) backwards, and add/sub first, then mult/div, then deal with exponents, then undo parentheses.  

 

I hope this helps.  :-)