What is the value of x in the proportion. x/2=16x-3/20 1. 2 2. -3/2 3. 1/4 4. 1/2

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What is the value of x in the proportion. x/2=16x-3/20 1. 2 2. -3/2 3. 1/4 4. 1/2

Mathematics
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\[\frac{x}{2} = \frac{16x-3}{20}\] is that how the problem reads?
yes
Do you know about cross-multiplication?

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Other answers:

yes
Good. Cross-multiply and solve the resulting equation for \(x\)
actually i am confused on how to cross multiply on this can you explain?
Okay, \[\frac{x}{2} = \frac{16x-3}{20}\] multiply the numerator of one by the denominator of the other \[x*20 = 2*(16x-3)\]\[20x = 32x - 6\]
What you are effectively doing is making a common denominator of 1
Can you solve \[20x = 32x - 6\] for \(x\)?
x=1/2
let's try it in the original equation and make sure it works: \[\frac{\frac{1}{2}}{2} = \frac{16(\frac{1}{2})-3}{20}\]\[\frac{1}{4} = \frac{8-3}{20}\]\[\frac{1}{4} = \frac{5}{20} = \frac{1}{4}\checkmark\]
Okay i get it now thanks!
Can you help me with one more?
We could also solve like this: \[\frac{x}{2} = \frac{16x-3}{20}\]Multiply both sides by 20\[20*\frac{x}{2} = 20*\frac{16x-3}{20}\]\[10x = 16x-3\]\[10x-10x+3 = 16x-10x+3-3\]\[3=6x\]\[x=\frac{1}{2}\]
Wait so 1/2 is the answer or 1/4?
the answer is x = 1/2. what I did was plug the value we got for x back into the original equation to make sure that it made a true statement. Let's say that I made a mistake somewhere and decided that \(x=2\) is the right answer. Well, when I plug that back into the original, I get: \[\frac{2}{2} = \frac{16(2)-3}{20}\]\[1 = \frac{29}{20}\]and that is not true, so that means that \(x=2\) is NOT the correct answer.
Ohhh okay thank you so much. I am gonna open another question can you help me?
sure, just "tag" me by putting "@whpalmer4" in a response and I'll get a notification

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