2 step algebra equations. For a 2 step algebra equation how do you know when you're supposed to add vs. subtract or multiply vs. divide?

Question

Step 1) Add or Subtract the necessary term from each side of the equation to isolate the term with the variable while keeping the equation balanced.

Step 2) Mulitply or Divide each side of the equation by the appropriate value solve for the variable while keeping the equation balanced.

Answer 1

You add or subtract values that aren't "attached" to variables via multiplication or division (e.g 4x, x/3). Then multiply or divide both sides once the variable-term is isolated to one side in a way to cancel out the attached factor.

Let's look at the following problem:

2x - 6 = -4

x in this case is multiplied by 2, then has 6 subtracted from it to equal -4.

We want to isolate x, so to get rid of minus 6 on the left, we add 6 to both sides to get:

2x = 2

We then want to get the factor of 2 off of x as well, so we divide both sides by 2 to get:

x = 1

To put it simply, to remove a term from one side of an equation, you must do the opposite action to both sides in order to cancel the desired term out. So subtract to get rid of an addition, divide to get rid of a multiplication, etc.

Answer 2

A simple rule to follow for this scenario is to used the widely known P.E.M.D.A.S. This stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. If you are ever lost on a problem with many different signs you can just follow this rule and you will always reach the answer.