+444 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.
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
+9479 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:
\(\frac34x+\frac58\ =\ 4x\\~\\ 8\big(\frac34x+\frac58\big)\ =\ 8\big(4x\big)\\~\\ 8\cdot\frac34\cdot x\ +\ 8\cdot\frac58\ =\ 8\cdot4\cdot x\\~\\ 6x\ +\ 5\ =\ 32x\\~\\ 5\ =\ 26x\\~\\ \frac{5}{26}\ =\ x\)_
