# Another dumb question, but: Why subtract 4z in 17z+9=7z+5? Why not divide by 4z?

#### spausm

##### New member
Ok so I'm not sure if this is just so obvious or I just missed this part of the lesson.
why am I subtracting on the first part and dividing on the second. why am I not dividing on both????

Just something I have accepted but hate that I dont really get it.
Thanks in advance hope everyone is having a great holiday!

#### Dr.Peterson

##### Elite Member
Ok so I'm not sure if this is just so obvious or I just missed this part of the lesson.
why am I subtracting on the first part and dividing on the second. why am I not dividing on both????

View attachment 10751

Just something I have accepted but hate that I dont really get it.
Thanks in advance hope everyone is having a great holiday!
It is really pretty simple: You subtract when you need to undo an addition (removing a term that is added), and you divide when you need to undo a multiplication (removing a coefficient that is multiplied).

#### Denis

##### Senior Member
why am I subtracting on the first part and dividing on the second. why am I not dividing on both????
IF you divided in first part, what would you divide by?

#### Otis

##### Senior Member
3z + 9 + 14z = 4z + 5

The goal is to isolate symbol z. That is, we need to manipulate the equation, until we have the form:

z = some constant

Before we isolate z, we need to combine like-terms. (After all, we cannot isolate symbol z, as long as it appears on both sides, right?) Therefore, combining like-terms involves adding and subtracting terms first.

After we combine all of the variable terms (on one side) and all of the constant terms (on the other side), we have:

13z = -4

Now we're ready to obtain a single z all by itself (form: z=constant); division does that for us (the final step).

You'll be solving many linear equations like this; with more practice, these steps will all seem natural. :cool:

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#### Jomo

##### Elite Member
Ok so I'm not sure if this is just so obvious or I just missed this part of the lesson.
why am I subtracting on the first part and dividing on the second. why am I not dividing on both????

View attachment 10751

Just something I have accepted but hate that I dont really get it.
Thanks in advance hope everyone is having a great holiday!
Note that 4 + 5 = 9 AND 9 - 4 = 5 And 9 - 5 = 4. Also 7 + 2 = 9 AND 9 - 2 = 7 AND 9 - 7 = 2.
Do you see a pattern???