How do you solve equations with variables on both sides?

Algebra
Tutor: None Selected Time limit: 1 Day

3d + 8 = 2d - 17

Sep 2nd, 2015

Thank you for the opportunity to help you with your question!

The goal is to get all the variables on one side, and all the constants on the other side.

3d+9=2d-17 

First let's subtract 2d from both sides, and simplify.

3d-2d+9=2d-2d-17

d+9=-17 

Now let's subtract 9 from both sides.

d+9-9=-17-9

d=-26

The problem is complete!


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 2nd, 2015

Oops, I noticed I wrote the wrong number

It would be d-8=-17-8

d=-25

Sep 2nd, 2015

This is thoroughly confusing because I don't even know what a variable is.

Sep 2nd, 2015

Okay, I will add more details.


Sep 2nd, 2015

Variables are represented by letters. So in this case, our variable is d.

We want to put all the d's on one side of the equation (= sign), and all the constants (which are the numbers without a variable) on the other.

We begin with the equation

3d+8=2d-17.

There are two options, you can either put all the variables on the left, or all the variables on the right. Whatever you do to one side of the equation, you HAVE to put it on the other side of the equation.

It is easier to find what will keep the equation positive.

So, I choose to put the variables on the left side.
In order to do so, I first check if 2d is positive or negative. Since it is positive, I need to subtract it. By subtract 2d (and I have to do it to both sides), I now have 0 on the right hand side.


3d-2d+8=2d-2d-17

1d+8=0-17

d+8=-17

Now, I use the same concept for putting the constants on the right side. I want the positive 8 to become zero, so I subtract 8 from both sides.

d+8-8=-17-8

d+0=-25

d=-25.


Does this make more sense?

Sep 2nd, 2015

-t + 5 = t - 19

Am I supposed to subtract the 19 from the 5?

Sep 2nd, 2015

-t+5=t-19

You have two options. You can subtract five from both sides, or you can add 19 to both sides.

Sep 2nd, 2015

how do you add a negative and a positive number?

Sep 2nd, 2015

You do not do both. I'm saying, you can either do

-t+5=t-19

-t+5-5=t-19-5

-t+0=t-24

-t=t-24 (Note this problem is not complete)

OR

-t+5=t-19

-t+5+19=t-19+19

-t+23=t-0

-t+23=t  (note this problem is not complete)

Sep 2nd, 2015

Typo

-t+24=t-0

-t+24=t

Sep 2nd, 2015

So the answer is 0?


Sep 2nd, 2015

Well, the answers are both invalid. Because we find that we have to subtract the t to a positive t. Which is 0. Since 0 cannot equal 24....It is false.

Sep 2nd, 2015

so do I write false on my paper?

Sep 2nd, 2015

You can, but typically we would write false. We would just say cannot complete, and say why.

Sep 2nd, 2015

Can you please explain why there is no solution? I am confused.

Sep 2nd, 2015

2 y+3 = 3 (y+7)

Sep 2nd, 2015

Sorry, I was working with another student. There is no solution because
the only number 0 can equal is 0.

0=0 is a true statement

0=1 is a false statement

0=2 is a false statement

0=3 is a false statement...and so on.

So, because the positive t and negative t cancel each other out, it leaves you with a 0.

It makes the statement 0= 24 false.

Sep 2nd, 2015

2y + 3 = 3 (y+7)

Sep 2nd, 2015

don't you multiply 3 by the 7 in parentheses  and then add the result to each side?

Sep 2nd, 2015

This is the last problem I will be helping you with. I will talk you through it.

You distribute the 3 to the y and the 7.

Tell me what you get when you do that.

Sep 2nd, 2015

wait I don't understand how to do that.

Sep 2nd, 2015

when you see a number such as 5(x+2), we distrubute the 5 to both the x and the 2.

Meaning we multiply by five to the x and multiply by five to the 2

5x+5(2)

5x+10.

Sep 2nd, 2015

That was just an example. Now do that for your problem.

Sep 2nd, 2015

how do you multiply by the letter?

Sep 2nd, 2015

Look at my example. A variable is a number, you just do not know which number. 5 *x =5x

Sep 2nd, 2015

2y + 3 = 3 (y+7)

2y+3=3*y+3*7

I have given you all the information you need to complete the problem. Unfortunately, I need to go to sleep.

Remember when there is a positive number, you want to make it 0 by subtracting.

When there is a negative number, you want to make it 0 by adding.

Sep 2nd, 2015

I am really confused about how to do that question

Sep 3rd, 2015

Do I add 2y +3 and get 5 and then subtract 3 from that side and get two?

Sep 3rd, 2015
2y+3=3*y+3*7 <=== First do the math for this step.


Sep 3rd, 2015

Picture 204.jpg    like this?

Sep 3rd, 2015

How did you get 19?  Isn't 21 minus 3 18?

Sep 3rd, 2015

Oops, Yes, it is 18. Sorry, math error.

Sep 3rd, 2015

Also how did you get fractions?  And Why didn't you subtract 3y from 2y and get 5y on the left side?

Sep 3rd, 2015

I meant negative 5 sorry

Sep 3rd, 2015

Because you do the opposite of what is listed so it becomes 0.

Sep 3rd, 2015

What? This is confusing.  How did you get fractions?


Sep 3rd, 2015

Thank You.  My error was that I had incorrectly subtracted 3 from 2.  Right?

Sep 3rd, 2015

-v + 5 +6 v = 1 + 5 v +3

Sep 3rd, 2015

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