how am I supposed to know when to subtract or add when doing algebraic equations?

Question

I am a little confused on knowing when to add or subtract in an equation. Example 3x-9=33 in this one you add 9 to 9 and 33 and in other similar equations you have to subtract. Please help me determine how to do the right thing!

Answer 1

In the equation 3x -9 = 33, you need to add 9 to the left side of the equation in order to eliminate the number from that side of the equation.  If you add 9 to the left side, you also need to add 9 to the right side otherwise you would change the equation.

 

Therefore, 3x - 9 = 33

add 9 to each side: 3x -9 + 9 = 33 + 9

solve: 3x = 42

x = 14

 

 

If you had the equation 3x + 9 = 33, you would subtract 9 from each side of the equation

Therefore, 3x + 9 - 9 = 33 - 9

3x = 24

x = 6

Answer 2

Nicole H. has given a very good explanation above; if the technical approach gives you trouble, another way of thinking about the process is to remember that we are trying to get the variable all by itself on one side of the equation.

Continuing with the above examples, let's say you had 3x-9=33 and you were trying to decide whether to add or subtract the nine (since that would leave the variable term, the one with the x, by itself on the left side of the equation). In order to cancel the -9 from the left side, we need to add a constant value that is would bring -9 to 0. We would symbolize this operation as -9 + ? = 0; obviously, +9 cancels -9, as anyone who has paid a debt knows. Since we added 9 to the left side, we must also add 9 to the right side of the equation in order to balance our equality. Historical note: this is the "reckoning", "al jabar", from which the word "algebra" is derived.

 

It is by this method of reasoning that we can determine whether to add or subtract while solving for a variable.