Question

Hardest question i ever face please i really need your help....

Answer 1

whats the question?

Answer 2

\[\frac{ 3x-2 }{ 4x} - \frac{ 2x+1 }{ 2x } =\frac{ 4 }{ 5 }\]

Answer 3

show your working please.

Answer 4

subtract

Answer 5

One way of doing this problem would be to focus ONLY on the two terms on the left side. They do not have the same denominator, so you must fix the 2nd term so that its denominator is the same as the that of the first term, 4x. How would you do that?\[\frac{ 3x-2 }{ 4x} - \frac{ 2x+1 }{ 2x }\] Focus on the 2nd term.

Answer 6

Raince: Please enclose the numerator of the 2nd term in parentheses. Then, multiply both the numerator and the denominator of that term by 2. What happens?

Answer 7

can i move -2 and +1 to the other side??.

Answer 8

multiply the second fraction top and bottom by 2, then the denominators will be the same and you can subtract

Answer 9

\[\frac{ 3x-2 }{ 4x} - \frac{ 2x+1 }{ 2x }\]
\[=\frac{ 3x-2 }{ 4x} - \frac{ 2x+1 }{ 2x }\times \frac{2}{2}\]\[=\frac{3x-2-2(2x+1)}{4x}\]

Answer 10

now clean up the numerators and "cross multiply"

Answer 11

\[x=\frac{ 4 }{ 5} + 17\] ???

Answer 12

the numerator is \[\frac{3x-2-2(2x+1)}{4x}\]
\[=\frac{3x-2-4x-2}{4x}\]\[\frac{-x-4}{4x}\]

Answer 13

\[\frac{-x-4}{4x}=\frac{4}{5}\]\[5(-x-4)=4\times 4x\] solve for \(x\)

Answer 14

Caution: Here we were working to combine those 2 terms on the left. Thankfully, satellie73 remembered to add the "=" sign and the fraction (4/5) on the right.

Answer 15

@raince: Use the distributive property of multiplication to multiply out 5(-x-4). Then equate your result to 4*4X on the right.

Answer 16

\[\frac{ 3x-2 }{ 4x } -\frac{ 2x+1 }{ 2x } = \frac{ 4 }{ 5 }\]
\[(5)\frac{ 3x-2 }{ 4x }-(10)\frac{ 2x+1 }{ 2x }=(4x)\frac{ 4 }{ 5 }\]
\[\frac{ 15x-10 }{ 20x }-\frac{ 20x+10 }{ 20x }=\frac{ 16x }{ 20x }\]
\[0=\frac{ 15x-10-(20x+10)-16x }{ 20x }\]
\[0=\frac{ -x-10-20x-10 }{ 20x }\]
\[0=\frac{ -21x-20x }{ 20x }\]
\[\frac{ 0 }{ 20x }=-21x-20\]
\[21x=20\]
\[x=\frac{ 20 }{ }\]
there are MULTIPLE answers to this, i think. at least this is what i got

Answer 17

oops x=20/21 as my final. not sure if it's right though

Answer 18

@dg98: Thank you. Would you please guide Raince towards checking this result (without actually doing the checking for him)? thank you. (Note: I get the same result, except for a different sign...but please lead Raince through that check anyway.)

Answer 19

@raince: we have spent a lot of time trying to solve\[\frac{ 3x-2 }{ 4x} - \frac{ 2x+1 }{ 2x } =\frac{ 4 }{ 5 }\] for x.

Our tentative result is x=20/21 (or x = -20/21.

It's very important to verify that one or the other is actually a solution. We do that by substituting the trial solution back into the original equation to determine whether that equation is now true or not. Have you done this kind of checking before?

Answer 20

yes i did but i didn't expect my working would be this hard. i try i followed the working which dg98 did and still can't find the way out the 20/21.