Solving Fractions: How to Solve x/36-x = 12/36-12 + 3.013/0.20(36-3.013)

[martine]

No homework, just a problem I'm faced with at work. And being the granny I am, this is ages ago since I solved anything like this.


x/36-x = 12/36-12 + 3.013/0.20(36-3.013)

The solution to this is 17.6. The question is: how do I solve such equations for x? If I ignore the 36 on the left side and asume it's not a fraction it's no problem, but um.. this is too long ago.

 

[betel]

Is the left hand side [tex] \frac{x}{36-x}[/tex] or [tex]\frac{x}{36} - x[/tex] ? I'm not sure where the fraction ends.
In the first case multiplying both sides by [tex] 36-x[/tex] will get you rid of the fraction, in the second case multiply with 36. Then you can use addition and subtraction to solve for x.

But no matter how i put the parenthesis in your equation i do not get the solution 17.6.

 

[seto6]

first add all like term like the one whit out the x, then isolate for x, then you will have the answer.

 

[Mark44]

No homework, just a problem I'm faced with at work. And being the granny I am, this is ages ago since I solved anything like this.


x/36-x = 12/36-12 + 3.013/0.20(36-3.013)

The solution to this is 17.6. The question is: how do I solve such equations for x? If I ignore the 36 on the left side and asume it's not a fraction it's no problem, but um.. this is too long ago.

What you have written is straightforward and unambiguous, but it might not mean what you intend. Writing fractional expressions as text on one line requires the use of parentheses for numerators or denominators that have multiple terms.

For x/36 - x, did you mean (x/36) - x or x/(36 - x)?
For 12/36 - 12 did you mean (12/36) - 12 or 12/(36 - 12)? The first is a negative number; the value of the second is 1/2.

For 3.013/0.20(36-3.013), did you mean (3.013/0.20) * (36 - 3.013) or 3.013/(0.20 *(36 - 3.013))?

 

[CellCoree]

Solving equations involving fractions can be tricky, but there are a few steps you can follow to make the process easier. First, we need to simplify both sides of the equation by finding a common denominator. In this case, the common denominator is 36. We can rewrite the equation as follows:

(x/36) - (x/36) = (12/36) - (12/36) + (3.013/0.20)(36/36 - 3.013/0.20)

Next, we can combine like terms on each side of the equation. On the left side, the x/36 and -x/36 cancel each other out, leaving us with 0. On the right side, we can simplify (12/36) - (12/36) to 0 and (36/36) to 1. This leaves us with:

0 = 1 + (3.013/0.20) - (3.013/0.20)

Now, we can simplify the fractions on the right side by dividing both the numerator and denominator by 0.20. This gives us:

0 = 1 + 15.065 - 15.065

Finally, we can combine the terms on the right side to get:

0 = 1

This equation is not true, which means there is no solution for x. Therefore, we can conclude that the original equation has no solution. If you encounter a similar problem in the future, remember to simplify both sides of the equation by finding a common denominator and then combine like terms to solve for x.