7/13x = 5/17 x=? The Best and Worst way to solve this BASIC ALGEBRA equation!

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[tomtke]

there's two possible interpretstions of this:
#1 (7)/(13x)=(5)/(17)
#2 (7/13)x=(5/17)
and they are different

#2:
x = (5/17)(13/7)
= 65/119

#1:
(7)/(13x)=(5)/(17)
13x=(7)(17)/(5)
x=(7×17)/(5×13)
= 119/65

ans.1 x = 65/119
ans.2 x = 119/65

[badalkumarlaskar]

I do not agree with the answer (65/119). It should be 119/65.

[Sailoralso]

The position of X IS unclear. There should have been parenthesis used to clarify.

[dazartingstall]

My Great Aunt's lodger's friend's cousin's boyfriend's pet snail did this in 0.0009 seconds, blindfolded, without the aid of a safety net. From beyond the grave. Which is surprising, because it only ever learned to read five words.
⁷⁄₁₃x = ⁵⁄₁₇
x = ⁵⁄₁₇ ÷ ⁷⁄₁₃
x = ⁶⁵⁄₁₁₉

[gavindeane]

"Let me just be clear here" he says, after writing stuff that's not very clear at all.

A lot of people would interpret that as

7

13x

Maybe use a vertical layout for fractions, or add some parentheses if you're going to use inline dividing with implied multiplication like this.

[johnnyragadoo]

Why not write it as 7x/13? 7(x/13) = (7x)/13. Write to communicate, in other words.

[VaTom]

Yeah, I read that as 7 over 13X not (7/13)X. 7X/13 would have been clear.

[Stylux-zp]

7 / 13x = 5 / 17 ---> is a ratio comparison so cross-multiplication ⤮ is applicable in this case
13x * 5 = 7 * 17
65x = 119
x = 119/65 = 1.8307 ---> ANS
falsification: 5 / 17 = 0.2941 and 7 / (13 *1.8307) = 0.2941 ----> Is not False
All paths lead to Rome.

[gregpoehlein]

I would like to point out that if you rounded off the initial decimals to three places, the significant digits rule applies, and the final result must also be to three places. If that rule is applied, the two solutions match. As John pointed out, though, keeping the numbers as fractions is the proper solution - I only use decimals in chemistry and/or physics.

[pikeoblisco]

The LHS shows 7/13x. To be pedantic (my speciality 😂) one could write (7/13)x. Or you could write a different fraction 7x/13 .… just saying’

[EricWells-sp]

At the outset, Mr. Zimmerman said "seven over 13x." He did NOT say "the quantity 7 divided 13 all multiplied by x." Everything he did following his initial statement was INCORRECT. The x is CLEARLY in the first DENOMINATOR!

[chrisdissanayake]

7 5
—— X = —-
13 17

The above is the same as,
7X 5
—- = ——
13 17
Cross multiplying,

7X * 17 = 13*5

7X = 13*5➗ 17

X = 13*5➗ 17➗ 7

X= 0.546

[Pootycat]

0:57 WRONG! If it were what you say, it would be "7x/13." 😝 I just thought I'd add, for those who might misinterpret this, "7x" is the numerator, "13, " the denominator.

[gregc.mariano]

The correct answer should be x= 119/65.
Cross multiplying you'll get 65x=119, hence x=119/65.
This time the teacher explained it wrongly.
He has to redo it so as not to mislead people.

[에스피-zg]

7/13x=5/17
35/65x=35/119
65x=119
x=119/65

[chrisdissanayake]

Yes, Mr John’s method is more admirable and it prevents a mistake that could happen if the fraction is taken wrong as 7➗ 13X rather than 7X➗ 13.

[panlomito]

This equation is not free of interpretation: is it (7/13) . x or 7 / (13x) I decided to follow the second .
7 / 13x = 5/17 will lead to 7 . 17 = 5 . 13x or 119 = 65 x so x = 119/65
What a nice answer!

But if we Pemdas this equation, reading from left to right it will be (7/13) . x so the answer will be the opposite
or x = 65/119

But I think this is not the purpose of math, it has to be clear for everyone and so perenthesis would be necessary.

[dazartingstall]

John, just to note: If you'd used the horizontal fraction bar (as you've advised is best practice in the past) like:
7
-- X
13
…you wouldn't have had to explain that you didn't mean 7/(13x).
Edit: Okay, it looks like you did it to make a point. Please ignore the above.

[Kualinar]

First step : Isolate the variable.
So (7/13)x = (5/17) → x = (13/7) * (5/17) → x = 65/119

[russelllomando]

got 119/65 the correct answer
13x X 5 = 65x 7 X 17 = 119 then divide by 65 - 119/65
119 / 65 = 1.83
1.83 X 13 = 23.8
7 / 23.8 = .2941
5 / 17 = .2941
Please explain???