Question

Solve for x:
((2/13x)+(1/4))=((95/26x)-(1/3)).
I know the solution set is 6, but I want to know how to get it.

Answer 1

May I help ?

Answer 2

@rrey

Answer 3

Sure, if you explain it well

Answer 4

Am I explain last bad ?

Answer 5

Kind of, but I still got it right

Answer 6

Did u get any answers ?

Answer 7

For the last one or this one? For the last one I got that the denominator cannot be zero, and the solution set is 6. This one, however, I can't figure out how to even start it.

Answer 8

We have to get Xs in a place and numbers in another :)
Got it ?:)

Answer 9

yeah. But I don't know how to do that right now

Answer 10

@Hero do you think you could help?

Answer 11

OK !
No problem :)
Look :

Just it :)

Answer 12

@rrey

Answer 13

Well, I'll go ahead and interpret it literally...

Answer 14

You have:
\[\frac{2}{13}x + \frac{1}{4} = \frac{95}{26}x - \frac{1}{3}\]

Answer 15

\[\frac{ 2 }{13x }+\frac{ 1 }{ 4}=\frac{ 95 }{ 26x }-\frac{ 1 }{ }\]

Answer 16

*over 3.

Answer 17

If that's it, then you definitely posted incorrectly horizontally. Observe how wolframalpha interprets it:
http://tr.im/4fmk8

Answer 18

Sorry. Well anyway, I still don't know what to do. I know in the end, my solution set will be 6 and x can't equal 0. But I don't know how to do the work

Answer 19

Every time a student posts fractions horizontally, I have to explain this before proceeding.

Answer 20

Don't worry. I will show you.

Answer 21

\[\frac{2}{13x}+\frac{1}{4}=\frac{95}{26x}-\frac{1}{3}\]

Multiply \(\dfrac{2}{13}\) by \(\dfrac{2}{2}\) to get
\[\frac{4}{26x}+\frac{1}{4}=\frac{95}{26x}-\frac{1}{3}\]

Subtract \(\dfrac{4}{26}\) from both sides; Add \(\dfrac{1}{3}\) to both sides:
\[\frac{1}{3}+\frac{1}{4}=\frac{95}{26x}-\frac{4}{26x}\]

Answer 22

Then add \(\dfrac{1}{3}\) and \(\dfrac{1}{4}\) while combing fractions on the right side to get:
\[\frac{7}{12} = \frac{91}{26x}\]

Answer 23

From there, you can cross multiply to continue solving

Answer 24

I would proceed in the following manner to make this as painless as possible:
\[7(26x) = 91(12)\]

\[\frac{26x}{12} = \frac{91}{7}\]
I re-wrote it this way because 91 is divisible by 7 and the fraction 26/12 is reducable:

\[\frac{13x}{6} = 13\]

Next, clearly we can divide both sides by 13 to get
\[\frac{x}{6} = \frac{13}{13}\]

Which the right side obviously cancels to:
\[\frac{x}{6} = 1\]

and muliplying both sides by 6 yields:
\[x = 6\]

Answer 25

Cool. Got it. Except I just cross multiplied and then did 1092/182x

Answer 26

But thank you very much. It helped a lot.

Answer 27

I prefer to deal with the smallest possible numbers. One general rule of algebra is to simplify whenever possible. In other words, the rules of algebra encourage you to reduce whenever the opportunity presents itself in order to avoid frustration and mistakes. Furthermore, I avoid having to depend on a calculator to simplify my result.

Answer 28

Hm. Well it's just freshman algebra and my teacher doesn't really restrict our calculating options so I figure I'll be okay. I'm not majoring in anything math-related anyway, but those are good tips. Thank you!