trouble with solving using laws of proportions

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evanr1234

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Hello Everyone,

(3-x)/(x+1) = 2/1. Solve for x. (answer is apparently 1/3)

(x+3)/10 = (3x-2)/8. Solve for x. (answer is 2)

The problems in my book do not have any parenthesis, I just added to avoid confusion. Please explain how to solve these problems using algebra, specifically the laws of proportions. Any help is greatly appreciated!
 
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evanr1234 said:
Hello Everyone,

(3-x)/(x+1) = 2/1. Solve for x. (answer is apparently 1/3)

(x+3)/10 = (3x-2)/8. Solve for x. (answer is 2)

The problems in my book do not have any parenthesis, I just added to avoid confusion. Please explain how to solve these problems using algebra, specifically the laws of proportions. Any help is greatly appreciated!
Click to expand...
Can you solve for "x" - if you are given:

2 * x + 2 = 3 - x
 
evanr1234 said:
Hello Everyone,

(3-x)/(x+1) = 2/1. Solve for x. (answer is apparently 1/3)

(x+3)/10 = (3x-2)/8. Solve for x. (answer is 2)

The problems in my book do not have any parenthesis, I just added to avoid confusion. Please explain how to solve these problems using algebra, specifically the laws of proportions. Any help is greatly appreciated!
Click to expand...
First, thanks for using parentheses; many students don't. They are necessary when you change from vertical fraction format to horizontal.

Now, what "laws of proportions" are you referring to? Do you mean "cross multiplication"? Have you tried that?
 
So I figured out the first one because:

I converted (3-x)/(x+1) = 2/1 to (3-x)/2 = (x+1)/1 (this is one of the laws of proportion)

then from here I quickly reached the step Khan showed me above.

I still am a little foggy on how I would know to choose that particular law first, but I suppose it could just be trial and error. I have not yet solved the second one but will try again soon. Thank you!
 
Are you familiar with cross-multiplication? I think that's far more direct than what you did; it converts directly (3-x)/(x+1) = 2/1 to (3-x) = 2(x+1), which is what Khan asked about! It will also work for the second probem.
 
(3-x)/(x+1) = 2/1
Then (x-3)/(x+1) = -2/1
Now x+1 is 4 more than x-3. In -2/1 the denominator is 3 larger than the numerator so think of -2/1 as (-2*4/3)/(1*4/3) = (-8/3)/(4/3) so we have the denominator 4 more than the numerator.

Now solve x+1 = 4/3 or x-3 = -8/3 (they both give the same result)
 
If \(\displaystyle \frac{a}{b}= \frac{c}{d}\), multiplying both sides by b, \(\displaystyle a= \frac{bc}{d}\) and then, multiplying both sides by d, \(\displaystyle ad= bc\), That's the "cross multiplication" Dr. Peterson mentioned.
 
Thank you everyone! I am able to solve both now. Cross multiplication was highly practical.
 
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