Fraction with an x: 1/3-x/5=1/2-x/10 (how to solve for x?)

I don't know where to begin, I know you have to find the common denominator, which is 30, but the x's are killing me. I don't know where to begin on this problem.

1/3-x/5=1/2-x/10
This is a fraction. I couldn't save it like it is supposed to look like.
it's 1 third minus x over 5 = 1 half minus x over 10

Can anyway get me started on finding the x
Or some way to solve this problem?

Re: Fraction with an x, HELP!

Why is it different than any other fraction.

1) Common denominator.
2) Add.

1/3
x/5
LCD = 15
5/15
3x/15

1/2
x/10
LCD = 10
5/10
x/10

Put is all back together.

Re: Fraction with an x, HELP!

bikersiggy said:

I don't know where to begin ... the x's are killing me.

Click to expand...

Hi bikersiggy:

Here's a question: How would you begin with this different problem?

\(\displaystyle $3 - x = 2x - 10$\)

Some people might say, "The first goal is to get all of the terms that contain X on one side of the equals sign, and the terms that do not contain X on the other side".

I would say that's a good idea for the problem that you posted, too.

\(\displaystyle \frac{1}{3} - \frac{x}{5} = \frac{1}{2} - \frac{x}{10}\)

Does it help to reduce the killing-effect of the Xs when you see your equation rewritten in this form?

\(\displaystyle \frac{1}{3} - (\frac{1}{5})x = \frac{1}{2} - (\frac{1}{10})x\)

In other words, perhaps it's not the Xs that are killing you; perhaps it's the fractions.

Let's add (1/10)x to both sides of the equation, and then subtract (1/3) from both sides. This will achieve the goal of getting all terms with an X on one side.

\(\displaystyle \frac{1}{10}x - \frac{1}{5}x = \frac{1}{2} - \frac{1}{3}\)

Is this enough help? If not, then please post whatever work you are able to accomplish, and let us know why you're stuck.

Cheers,

~ Mark

Re: Fraction with an x, HELP!

They still don't = because the common denominator is 30
so it would be 10/30 - 6x/30 = 15/30 - 10x/30 that would = 4x/30 = 5x/30, so they don't equal. What am I doing wrong?

Re: Fraction with an x, HELP!

bikersiggy said:

They still don't = because the common denominator is 30
so it would be 10/30 - 6x/30 = 15/30 - 10x/30 that would = 4x/30 = 5x/30, so they don't equal. What am I doing wrong?

Click to expand...

Biker, you are NOT being careful: that is WRONG.

We start with: 1/3 - x/5 = 1/2 - x/10
That becomes: 10/30 - 6x/30 = 15/30 - 3x/30 : HOW did you get - 10x/30 ?!
Then that becomes: 10 - 6x = 15 - 3x (since all denominators are the same)
Then: 6x - 3x = 10 - 15
Then: 3x = -5
Then: x = -5/3

Your statement: "4x/30 = 5x/30, so they don't equal" makes absolutely no sense...
You need a private tutor. Your "ramblings" are just about impossible to handle at a site like this one.

Re: Fraction with an x, HELP!

Your right Denis, I probably do need a tutor. I just thought they had to equal because there was an equal sign. I am getting better every day, I have been studying like crazy. I had to go back to the algebra basics, so I could get a better handle on what I was doing in the first place. I do aprreciate your help, and I have learned from you and others on this site. Maybe someday I will be good enough at this to answer questions too. I am humbled by your ability and wish I had your knowledge. Thank you very much for the help. I have found if I really look at the problems and take my time instead of hurrying through them I do much better. I am getting things down better, now working on figuring out the positive and negative aspects of problems. That's my next step to working out better equations.
I do understand how you got 30, and had did that part, I was confused on the x part, as I am learning the basic functions of algebra, I am starting to understand that part too. I truly do appreciate the time you ahve taken to help me.

Re: Fraction with an x, HELP!

bikersiggy said:

What am I doing wrong?

Click to expand...

That's a hard question to answer without observing your work. One answer may be that you're not checking your work.

bikersiggy said:

... so it would be 10/30 - 6x/30 = 15/30 - 10x/30 ...

Click to expand...

What you typed implies that you did this:

\(\displaystyle \frac{3}{3} \times \frac{x}{10} = \frac{10x}{30}\)

This is false because 3 times X is not the same as 10 times X. You are the only person who can determine if and why you made this mistake.

bikersiggy said:

... that would = 4x/30 = 5x/30 ...

Click to expand...

What you typed implies that you did this:

\(\displaystyle \frac{15}{30} - \frac{10}{30} = \frac{5x}{30}\)

This is false because 15 minus 10 equals 5, not 5x. You are the only person who can determine if and why you made this mistake.

bikersiggy said:

What am I doing wrong?

Click to expand...

I suspect that you already possess sufficient smarts to know how to check your work and that you would have found these mistakes with mental effort. Maybe the answer to your question is that you're not checking your work.

Cheers,

~ Mark

Re: Fraction with an x, HELP!

Biker, say you have: 3x / 5 = 2x / 4 + 1

x is a number (that we need to find) that causes each side to be equal; OK?

We see that the LCD (Lowest Common Denominator) is 20; OK?

So we simply need to multiply EACH term by 20:
(3x / 5) * 20 = 12x
(2x / 4) * 20 = 10x
1 * 20 = 20
So we now have: 12x = 10x + 20
Then: 2x = 20
x = 10

Now, if you substitute 10 for x in the original equation:
3(10) / 5 = 2(10) / 4 + 1
30 / 5 = 20 / 4 + 1
6 = 5 + 1
6 = 6
So this PROVES that x = 10 is correct.

You kapish now ? :wink: