Question

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

Answer 1

\[\frac{x}{2} = \frac{16x-3}{20}\]
is that how the problem reads?

Answer 2

yes

Answer 3

Do you know about cross-multiplication?

Answer 4

yes

Answer 5

Good. Cross-multiply and solve the resulting equation for \(x\)

Answer 6

actually i am confused on how to cross multiply on this can you explain?

Answer 7

Okay,
\[\frac{x}{2} = \frac{16x-3}{20}\]

multiply the numerator of one by the denominator of the other

\[x*20 = 2*(16x-3)\]\[20x = 32x - 6\]

Answer 8

What you are effectively doing is making a common denominator of 1

Answer 9

Can you solve \[20x = 32x - 6\] for \(x\)?

Answer 10

x=1/2

Answer 11

let's try it in the original equation and make sure it works:

\[\frac{\frac{1}{2}}{2} = \frac{16(\frac{1}{2})-3}{20}\]\[\frac{1}{4} = \frac{8-3}{20}\]\[\frac{1}{4} = \frac{5}{20} = \frac{1}{4}\checkmark\]

Answer 12

Okay i get it now thanks!

Answer 13

Can you help me with one more?

Answer 14

We could also solve like this:

\[\frac{x}{2} = \frac{16x-3}{20}\]Multiply both sides by 20\[20*\frac{x}{2} = 20*\frac{16x-3}{20}\]\[10x = 16x-3\]\[10x-10x+3 = 16x-10x+3-3\]\[3=6x\]\[x=\frac{1}{2}\]

Answer 15

Wait so 1/2 is the answer or 1/4?

Answer 16

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.

Answer 17

Ohhh okay thank you so much. I am gonna open another question can you help me?

Answer 18

sure, just "tag" me by putting "@whpalmer4" in a response and I'll get a notification