Thread: Solve for the given variable:

1. Solve for the given variable:

I'm having trouble with these problems. Every time I see a fraction I get lost in these kind of equations.

Here is my first equation:

3x+4/x-2 = 5/6

and here is the second one:

8t - 6t-1/2 = 5

EDIT:
I apologize, I wrote my problems wrong!

This how they should be:

$
\frac{3x+4}{x-2} = \frac{5}{6}
$

And this is the second one:

$
8t-\frac{6t-1}{2} = 5
$

Sorry, thanks for the help in advance!

2. $3x+\frac{4}{x}-2 = \frac{5}{6}$

Multiply both sides through by x

$3x^2+4-2x = \frac{5x}{6}$

That removed the fraction part in the second term.

Now multiply through by 6

$18x^2+24-12x = 5x$

$18x^2+24-17x = 0$

now you have a quadratic, can you solve this?

3. Thanks for the quick reply but I think you misunderstood my problem. I apologize, I wrote it incorrectly.
This is how it should look:

$
\frac{3x+4}{x-2} = \frac{5}{6}
$

And this is the second one:

$
8t-\frac{6t-1}{2} = 5
$

I apologize, thank you for the help though.

4. Originally Posted by Somatic
I'm having trouble with these problems. Every time I see a fraction I get lost in these kind of equations.

Here is my first equation:

3x+4/x-2 = 5/6

and here is the second one:

8t - 6t-1/2 = 5

Fractions are our friends!

Just think of them as numbers. Look, if you don't like the fractions, replace it with a letter until the rest of the problem is done. Then, when you solve for x, put the fraction where it's supposed to go. It's like a crutch until you get it.

Check out the second problem.

if I pretend that 1/2 is $(a)$ for a minute, the I have

$8t-6t-(a)=5$

Now, we want to get t by itself, so notice that $8t$ and $6t$ are like terms, so we can combine them like this

$2t-(a)=5$

Now let's add $(a)$ to both sides

$2t=5+(a)$

Now we divide both sides by two, and we have t alone at last

$t=\frac{5+(a)}{2}$

Now would be a good time to put the fraction back where $(a)$ is

$t=\frac{5+1/2}{2}$

Now, simplify the numerator

$\frac{5+1/2}{2}=\frac{\frac{10}{2}+\frac{1}{2}}{2}=\frac{\fr ac{11}{2}}{2}$

Now, I know this look crazy, but if you think about it

$\frac{\frac{11}{2}}{2}=\frac{11}{2}\div\frac{2}{1} =\frac{11}{2}\cdot\frac{1}{2}=\frac{11}{4}$

Therefore

$t=\frac{11}{4}$

This may confuse the heck out of you, but its another way to do things.

Bye!

5. Sorry guy!
I edited my first post, they have the correct equation. I wasn't sure on how to use the math tags. I'm sorry if I confused you all.
Thanks for the help though, I appreciate it!

Can someone give me a start on my problems please, thank you for the above posters for the help either way.

6. $\frac{3x+4}{x-2} = \frac{5}{6}$

$6(3x+4) = 5(x-2)$

Now expand and group like terms.

7. Wow, thank you pickslides. I tend to over think things when I don't know how to begin these types of equations. I got my solution to the first problem which is:

$x = \frac{-34}{13}$

I am trying to solve the next one but I think I'm doing a step wrong.

$8t - \frac{6t-1}{2} = 5$

I canceled the 2 by multiplying then I multiplied the other numbers as well.
$16t-6t+1 = 10$

The 1 changes to a positive correct?

Am I on the right track?

EDIT:

I solved it.
I continued and did this.
$10t+1 = 10$

End result :
$t = \frac{9}{10}$

Now I have another problem that really throws me off.

This:
$\frac{4}{x} - \frac{x}{8} = 0$

Just give me a step please I want to try to solve but I don't know where to start.
Thanks for the support!

8. Originally Posted by Somatic

I am trying to solve the next one but I think I'm doing a step wrong.

$8t - \frac{6t-1}{2} = 5$

I canceled the 2 by multiplying then I multiplied the other numbers as well.
$16t-6t+1 = 10$

The 1 changes to a positive correct?

Am I on the right track?

EDIT:

I solved it.
I continued and did this.
$10t+1 = 10$

End result :
$t = \frac{9}{10}$
Sounds good to me

9. $\frac{4}{x} - \frac{x}{8} = 0$

multiply both sides by x gives

$4 - \frac{x^2}{8} = 0$

Can you solve this?

10. Originally Posted by pickslides
$\frac{4}{x} - \frac{x}{8} = 0$

multiply both sides by x gives

$4 - \frac{x^2}{8} = 0$

Can you solve this?
Okay, I'm not sure if I'm doing this correctly.

I then multiplied both sides by 8 giving me this:

$4 - x^2 = 0$

After this continued with adding 4 to both sides got this:

$-x^2 = 4$

Is this my answer? I'm pretty sure I'm off big time. Please elaborate on what I did wrong, if I am incorrect.

$x = - \sqrt(4)$

11. You had the right idea, but didn't execute it too well.

$4 - \frac{x^2}{8} = 0$

both sides by 8 gives

$32 - x^2 = 0$

then

$32 = x^2$

$x^2 = 32$

$x = \pm\sqrt{32}$