Algebra Rational Expression Question: solve equation X - 2/4 - (x - 3/4)

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tathagata7

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Hello,

I'm trying to solve the following equation:

X - 2/4 - (x - 3/4)

I know the answer is: 1 - 3X / 4

I'm trying to derive the answer I know I need to add the 3/4 but I cannot figure this out.

X - 2/4 - X + 3/4 is where I got.

Thank you,

Carrie
 
tathagata7 said:
I'm trying to solve the following equation:

X - 2/4 - (x - 3/4)

I know the answer is: 1 - 3X / 4
Click to expand...
Then the instructions cannot possibly been to "solve the equation", since this is only an expression (having no "equals" sign in it) which cannot be "solved". Are you maybe supposed to "simplify"?

tathagata7 said:
I'm trying to derive the answer I know I need to add the 3/4 but I cannot figure this out.

X - 2/4 - X + 3/4 is where I got.
Click to expand...
I will guess that "x" is meant to be "X". But I'm not sure I'm understanding where you're getting stuck in combining -2/4 and +3/4, or in combining the +X and the -X. You've posted this to "Intermediate / Advanced Algebra", which means you've already studied beginning algebra like "x - x" and pre-algebra like "-2 + 3". So clearly I'm missing something...? :oops:
 
Last edited:
Clarification

The problem read which expression is equivalent to:

(X-2)/4 - (X - 3/4)

The answer on the exam is: (1 - 3X) / 4
 
Okay, so you were able to get to this point:

\(\displaystyle \dfrac{x-2}{4}-x+\dfrac{3}{4}\)

What happens if you find a common denominator and then subtract straight across?
 
tathagata7 said:
Hello,

I'm trying to solve the following equation:

X - 2/4 - (x - 3/4)

I know the answer is: 1 - 3X / 4

I'm trying to derive the answer I know I need to add the 3/4 but I cannot figure this out.

X - 2/4 - X + 3/4 is where I got.

Thank you,

Carrie
Click to expand...
Your problem appears to be grouping symbols. As you have written the expression X - 2/4 - (x - 3/4) [assuming x and X represent the same thing] we have
\(\displaystyle X\, -\, \dfrac{2}{4}\, -\, (X\, -\, \dfrac{3}{4})\)
and the 'proper answer' 1 - 3X / 4 is
\(\displaystyle 1\, -\, \dfrac{3X}{4}\). Actually your answer X - 2/4 - X + 3/4 [ =1/4 ] is the proper answer for the original expression as written.

However, I believe the grouping symbols are different. That is, if you had
\(\displaystyle \dfrac{X-2}{4}\, -\, (X\, -\, \dfrac{3}{4})\)
you would write that as (X-2)/4 - (X - 3/4). The 'simplified' expression would then be (1-3X)/4.
 
Clarification

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attachment.php


Thank you for very much for helping. I've attached an image of my problem and answer. My confusion is how to get to the 3x I can see how I got the 1/4 portion of the answer.
 

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tathagata7 said:
attachment.php

attachment.php


Thank you for very much for helping. I've attached an image of my problem and answer. My confusion is how to get to the 3x I can see how I got the 1/4 portion of the answer.
Click to expand...

(x-2)/4 -(x - 3/4) = x/4 - 2/4 - x + 3/4 = (-x + x/4) + ( 3/4 - 2/4) = -3/4 * x + 1/4 .... continue...
 
Subhotosh Khan said:
(x-2)/4 -(x - 3/4) = x/4 - 2/4 - x + 3/4 = (-x + x/4) + ( 3/4 - 2/4) = -3/4 * x + 1/4 .... continue...
Click to expand...

Thank you.

I understand (-x + x/4) + (3/4 - 2/4)

= (-x + x/4) + (1/4)

how do you get the to the 3/4 in the 3/4*x from (-x + x/4) ?
 
tathagata7 said:
Thank you so much Jomo. I understand now.

= x(-1 + 1/4)
= x(-4/4 + 1/4)
= x(-3/4)
= -3x/4
add the 1/4 to derive the answer: 1-3x/4\(\displaystyle \ \ \ \ \ \ \ \ \)That is incorrect. **

:-D
Click to expand...

1/4 + (-3x/4) =

(1 - 3x)/4



** What you have equals \(\displaystyle \ \ 1 \ - \ \dfrac{3x}{4}.\)
 
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