Question

Hello everyone. I'm very confused on how this algebra calculator is solving this equation. How I was taught (and forgot about it) and how this calculator is solving it is two different ways. I'm not familiar with how the calculator is solving it and I need some help on this. Can you please help me? (Equation in the comments).

Answer 1

Start from what you know, how would you have gone about solving it?

Answer 2

I would have started by adding 3x to itself and to the right side of the equation, making it 3x + 3x - 2y = 12 + 3x. Afterwards, 3x + 3x cancels itself out, making it -2y = 12 +3x. Then I'd deal with 12 +3x, but I'm not too sure how to. That's when I went to the calculator and decided to ask for help.

Answer 3

We start with \(\large 3x - 2y = 12\)

If we were to ADD 3x to both sides...we arrive at:

\[\large 3x + 3x - 2y = 12 + 3x\]
Which comes out to
\[\large 6x - 2y = 12 + 3x\]

Hasn't really gotten us anywhere

Answer 4

But this is for a graph, and I thought since we were previously subtracting 3x from 2y, the opposite would have to be done and add it instead of subtracting. I thought that true for all equations solving for a variable.

Answer 5

You have it a little mixed up...but that's okay :)

Think about a simple problem

\[\large x + 2 = 5\]

Here, we want 'x' by itself on one side of the '=' sign...now obviously we know the answer is 3 (because 3 + 2 = 5) right? But how did we get there?

Since 2 is being ADDED to 'x'....we must undo that by SUBTRACTING 2 from both sides...

\[\large x + 2 - 2 = 5 - 2\]
or
\[\large x = 3\]

Answer 6

So going back to the original question

\[\large 3x - 2y = 12\]

We FIRST want -2y by itself on one side of the '=' sign...so notice that \(\large 3x\) is being ADDED to that \(\large -2y\) right?

So that means we need to SUBTRACT 3x from both sides of the equation

Answer 7

So when on the right side we get 12 - 3x, that's like saying 12 + (-3x), right?

Answer 8

Correct :)

Answer 9

Exactly as the calculator stated....just remembering that Adding -3x ....and subtracting 3x are the same thing!

Answer 10

So then we get -2y = 9, and they divide both sides be 2?

Answer 11

Not quite...we cannot simply combine the 12 and the -3x like that.

\[\large -2y = 12 - 3x\]

We can only combine 'like terms' meaning we can only combine that 3x with other terms that have 'x'...not the case here

Here, the only other thing to do is completely isolate that 'y'...and that is why the calculator showed dividing both sides by -2

Answer 12

Ahhh, alright, now I see. But now I have a question (since I have YET to master fractions 100%). \[\frac{ -3x + 12}{ -2 }\]
How does that become \[\frac{ 3 }{ 2 }x-6\]

Answer 13

ANY time you have a fraction that has an operation happening in the numerator (Like here, you are adding -3x and 12) you can break up the fraction...Meaning:

\[\large \frac{-3x + 12}{-2} \rightarrow \frac{-3x}{-2} + \frac{12}{-2}\]

Which of course leads to that \(\large \frac{3}{2}x -6\)

Answer 14

Oh my gosssshh, thank you so much. Now I understand clearly, and hopefully I can remember this for previous equations.

Answer 15

I have a whole other part of this question, though, with a graph. But I really didn't understand this part. Hopefully I can understand it now. But can I come back to you if I don't?

Answer 16

Absolutely! And don't worry, it comes with practice! Soon you'll be a senior in college engineering like me and stuff like this will be nothing! :)

And to answer your question...sure, If I'm around that is lol

Answer 17

Thank you so much. I hope to be an engineer! That would be pretty cool. One day it'll be all easier.

Answer 18

could anyone help me on a geometry problem pleaseeee?