This is probably an easy one but...

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Rkonczyk

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So take this equation: 6=(15*x)/(15+x)
Now apparently the answer is x=10, but i require an explanation on how u get there. Also, is there a name for this type of equation? I think it would help if i could google it and get more practice
 
Hello, and welcome to FMH! :)

Begin with the given equation:

[MATH]6=\frac{15x}{15+x}[/MATH]
Observe that \(x\ne-15\) and multiply by \(x+15\)

[MATH]6(x+15)=15x[/MATH]
Divide by 3:

[MATH]2(x+15)=5x[/MATH]
Distribute on the LHS:

[MATH]2x+30=5x[/MATH]
Subtract \(2x\)

[MATH]30=3x[/MATH]
Divide by 3 and arrange as:

[MATH]x=10[/MATH]
 
Wow i right, it was easy lol that's a whole lot simpler than how they did it in the engineering book i was reading when i came across this. Thanks!
 
They went from

6(15+x)=15*× to
90+6x=15x then
15x-6x=90
9x=90
X=10

And they made absolutely no attempt to explain it. In case you were curious, the original equation is based on a formula to find resistances in a parallel electrical circuit. I'm trying to teach myself electrical engineering but its been a while since highschool algebra
 
An engineering textbook is likely going to assume a solid background in algebra. I'm surprised it gave that many steps.
 
Rkonczyk said:
They went from

6(15+x)=15*× to
90+6x=15x then
15x-6x=90
9x=90
X=10

And they made absolutely no attempt to explain it.
Click to expand...
This is actually the same process that @MarkFL used in this post to solve this, except that the "distribution" step was performed earlier. It is in fact sufficient for demonstrating the process, as long as you can follow what happens from one step to the next.

Let's look at each item individually, then figure out what must have happened in-between...

[MATH]6 = \frac{15x}{15+x}[/MATH]​

This is the problem as initially stated.

[MATH]6(15 + x) = 15x[/MATH]​

This was found by multiplying both sides of the equation by [MATH]15 + x[/MATH]. Since the right side was a fraction with that as the denominator, it effectively undoes the fraction, leaving only the numerator. On the left side, it was simply a matter of multiplying with 6.

[MATH]90 + 6x = 15x[/MATH]​

Here, the multiplication on the left side was performed, and the right side was left unmodified. [MATH]a(b + c)[/MATH], when distributing, becomes [MATH]ab + ac[/MATH]. The 90 comes from the fact that [MATH]6 * 15 = 90[/MATH].

[MATH]15x - 6x = 90[/MATH]​

In this step, [MATH]6x[/MATH] was subtracted from both sides of the equation (giving [MATH]90 = 15x - 6x[/MATH]), then the sides were exchanged with one another. The logic is that all of the [MATH]x[/MATH] terms need to be together in order to solve for [MATH]x[/MATH].

[MATH]9x = 90[/MATH]​

This is the result of subtracting [MATH]15x - 6x[/MATH] on the left, without doing anything on the right.

[MATH]x = 10[/MATH]​

Finally, we divide both sides by 9 to solve for [MATH]x[/MATH].
 
I do have one more question that i just realized. Going back to markfl's original explanation, did we divide by 3 because its lowest common denominator or the highest?
 
I divided by 3 because at that point 3 was the greatest common factor present on both sides. I did this primarily to make the numbers smaller when distributing in the next step.

You want to be careful when dividing by any expression that contains the variable, because you may be removing a solution when doing so, if it is possible for that expression to be zero. Since it isn't possible for 3 to be 0 (even for small values of 3), we can do so without worry. :)
 
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