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# Hello I'm having trouble on what to do first with this fractional 1 varible equation's

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I'm giving the equation Solve for x:$$\frac{3}{4}​​x + ​ ​\frac{5}{8} = 4x$$  Note that 3/4 and x are rigth next to each other like this 3/4x I had some trouble with the latex this time...

x = __________________ Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar.

Answer blank 1: Thank you so much for all the time spent to help me and to understand this concept better.

Jun 16, 2019
edited by HiylinLink  Jun 16, 2019

#1
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Solve for x:
(3 x)/4 + 5/8 = 4 x

Put each term in (3 x)/4 + 5/8 over the common denominator 8: (3 x)/4 + 5/8 = (6 x)/8 + 5/8:
(6 x)/8 + 5/8 = 4 x

(6 x)/8 + 5/8 = (6 x + 5)/8:
(6 x + 5)/8 = 4 x

Multiply both sides by 8: or: cross multiply
6 x + 5 = 32 x

6x - 32x = -5

- 26x = - 5                      multiply both sides by -1

x =5 / 26

Jun 16, 2019
edited by Guest  Jun 16, 2019
#2
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Thank you for the effort  and how you presented it but I'm having trouble understanding how you went from 3x to 6x....

Guest Jun 16, 2019
#5
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he/she multiplied the whole fraction by 2... does that help?

NoobGuest  Jun 17, 2019
#3
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It appears there are four "zero-width space" characters in your LaTeX code. Two of them are between the  3/4  and the  x  which is why it doesn't look normal. I found that out by pasting your code into this website: https://www.soscisurvey.de/tools/view-chars.php

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As for your actual question, this is pretty much the method guest used:

$$\frac34x+\frac58=4x$$

And  $$\frac34x=\frac{3x}{4}$$  so we can rewrite it like this...

$$\frac{3x}{4}+\frac58=4x$$

To get a common denominator, we can multiply  $$\frac{3x}4$$  by  $$\frac22$$  which won't change its value.

$$\frac22\cdot\frac{3x}4+\frac58=4x$$

And  $$\frac22\cdot\frac{3x}4=\frac{6x}8$$     ←That's how it went from  3x  to  6x

$$\frac{6x}8+\frac58=4x$$

Now that the fractions have a common denominator we can combine them.

$$\frac{6x+5}{8}=4x$$

Multiply both sides of the equation by  8

$$6x+5=32x$$

Subtract  6x  from both sides.

$$5=32x-6x$$

$$5=26x$$

Divide both sides by  26

$$\frac5{26}=x$$

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Also, we could multiply both sides of the equation by  8  to begin with, like this:

$$\frac34x+\frac58\ =\ 4x\\~\\ 8\big(\frac34x+\frac58\big)\ =\ 8\big(4x\big)\\~\\ 8\cdot\frac34\cdot x\ +\ 8\cdot\frac58\ =\ 8\cdot4\cdot x\\~\\ 6x\ +\ 5\ =\ 32x\\~\\ 5\ =\ 26x\\~\\ \frac{5}{26}\ =\ x$$_

Jun 16, 2019
#4
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Wow, thanks soo much that really explains alot of questions...

$$\dfrac{3}4 x + \dfrac{5}8 = 4x\\ 6x + 5 = 32x\\ 26x = 5\\ x = \dfrac{5}{26}$$