# Thread: Help a Dummy Figure Out An Easy Equation!

1. ## Help a Dummy Figure Out An Easy Equation!

Stupid me forgot how to solve equations with two variables. I tried finding a tutorial of some sort on the internet but I can't find one like the question I present to you here:

2 + 14x = 9x

For some reason I can't seem to find any tutorials on questions where the variable is on both sides of the = sign. Please help! I have absolutely no clue how to start off the solving process.

2. Originally Posted by SomeRandomPerson
Stupid me forgot how to solve equations with two variables. I tried finding a tutorial of some sort on the internet but I can't find one like the question I present to you here:

2 + 14x = 9x

2 + 14x - 14x = 9x - 14x

2 = -5x

can you finish?

For some reason I can't seem to find any tutorials on questions where the variable is on both sides of the = sign. Please help! I have absolutely no clue how to start off the solving process.
...

3. Originally Posted by SomeRandomPerson
Stupid me forgot how to solve equations with two variables. I tried finding a tutorial of some sort on the internet but I can't find one like the question I present to you here:

2 + 14x = 9x

For some reason I can't seem to find any tutorials on questions where the variable is on both sides of the = sign. Please help! I have absolutely no clue how to start off the solving process.
Write 14x in terms of 9x

2+14x=9x

2+5x+9x=9x

(2+5x)+9x=0+9x

2+5x=0

4. @skeeter: Thanks for the reply. I can finish it off, I think:

-5/2 = -2.5

x = -2.5

Is that right?

I'll do another one, please tell me if I'm wrong:

7x - 3 = 4x

3 - 7x + 7x = 4x + 7x

3 = 11x

3/11 = 3.66667

x = 3.66667

I really do appreciate the help! Please do tell me if i did it right.

Edit: Didn't see your reply there Archie. I'm not quite understanding your approach. Where did the 0 come from?

Another edit: I'm really confused now. From what I took from you skeeter, I got -2.5. But if I replace x with 2.5, the equation doesn't make sense:

2 + 14x = 9x

2 + 14(-2.5) = 9(-2.5)

2 + -35 = -22.5

-33 = -22.5

Obviously -33 isn't the same as -22.5... sorry if I'm missing something, I'm really having a hard time understanding this.

5. -5x = 2

x = -2/5 not -2.5

6. Does that mean for my second equation that I posted above the answer would be 3/11?

Also, what does a number with a slash represent? Is it like a fraction? I thought a slash meant to divide.

7. Originally Posted by SomeRandomPerson
@skeeter: Thanks for the reply. I can finish it off, I think:

-5/2 = -2.5

2=-5x

Divide both sides by -5

x=-2/5=-0.4

x = -2.5

Is that right?

I'll do another one, please tell me if I'm wrong:

7x - 3 = 4x

3 - 7x + 7x = 4x + 7x

You should have 7x-3=4x

7x-4x-3=4x-4x

3x-3=0

3x=3

3 = 11x

3/11 = 3.66667

x = 3.66667

I really do appreciate the help! Please do tell me if i did it right.

Edit: Didn't see your reply there Archie. I'm not quite understanding your approach. Where did the 0 come from?

We can say 4+0=4, x+0=x, adding zero does not change any value, therefore the 2+5x had to be 0

Another edit: I'm really confused now. From what I took from you skeeter, I got -2.5. But if I replace x with 2.5, the equation doesn't make sense:

2 + 14x = 9x

2 + 14(-2.5) = 9(-2.5)

2 + -35 = -22.5

-33 = -22.5

Obviously -33 isn't the same as -22.5... sorry if I'm missing something, I'm really having a hard time understanding this.
.

8. Originally Posted by SomeRandomPerson
Does that mean for my second equation that I posted above the answer would be 3/11?

Also, what does a number with a slash represent? Is it like a fraction? I thought a slash meant to divide.
2/5 is the same as $\displaystyle \frac{2}{5}$ is the same as $\displaystyle 2 \div 5$

you need some lessons ... go through all 4 pages of the following link

http://www.purplemath.com/modules/solvelin.htm

9. @Skeeter: Thanks a bunch for your help, and for the link. I will look at it.
@Archie: I get your 0 approach now. I'm a little confused about this though:

You should have 7x-3=4x

7x-4x-3=4x-4x

3x-3=0

3x=3
So x = 1 which is fine with me. But I'm confused as to how to start the equation. I thought you just move the number over and then do the opposite operation, which is why I used addition. Basically, my question is how do you start it, and how do you know which operation to use? What order do you put it in? How would I know what order to put it in?

Gah, I never thought such simple questions would cause so many problems with me!

10. Originally Posted by SomeRandomPerson
@Skeeter: Thanks a bunch for your help, and for the link. I will look at it.
@Archie: I get your 0 approach now. I'm a little confused about this though:

So x = 1 which is fine with me. But I'm confused as to how to start the equation. I thought you just move the number over and then do the opposite operation, which is why I used addition.

But you didn't do the opposite operation for the 7x. Let's look at that....

7x-3=4x

You want to find x. If we subtract 4x from both sides, we will get x on one side only

+7x-3=+4x

+7x-3-4x=+4x-4x

7x-4x-3=0

You can do that more quickly by bringing 4x to the other side and changing it's sign.

7x-3=4x

7x-4x-3=0

so we get 3x-3=0

Alternatively, you can subtract 7x from both sides

7x-3=4x

7x-7x-3=4x-7x

-3=-3x

Basically, my question is how do you start it, and how do you know which operation to use? What order do you put it in? How would I know what order to put it in?

You simply perform the OPPOSITE OPERATION on the x term you want to move.

7x-3=4x

+7x-3=0+4x

If you want to bring the x's together, you can subtract 4x from both sides to get no x on the right
or subtract 7x from both sides to get no x on the left.

Alternatively, write 7x as 3x+4x

7x-3=4x

3x+4x-3=4x

4x+(3x-3)=4x+0

3x-3=0

Two values are equal, when you subtract them the answer is 0.

3x=3

3(1)=3 so x=1, or divide both sides by 3.

Multiplying x by 3 gives 3, so perform the opposite operation. Divide both sides by 3 to get x.

3x=3

3x/3=3/3

x(3/3)=3/3

x(1)=1 so x=1

Gah, I never thought such simple questions would cause so many problems with me!
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