Solve for x:
4 + 2/x = 5 + 5/(3 x)
5 + 5/(3 x) = 5 + 5/(3 x):
4 + 2/x = 5 + 5/(3 x)
Bring 4 + 2/x together using the common denominator x. Bring 5 + 5/(3 x) together using the common denominator 3 x:
(2 (2 x + 1))/x = (5 (3 x + 1))/(3 x)
Cross multiply:
6 x (2 x + 1) = 5 x (3 x + 1)
Expand out terms of the left hand side:
12 x^2 + 6 x = 5 x (3 x + 1)
Expand out terms of the right hand side:
12 x^2 + 6 x = 15 x^2 + 5 x
Subtract 15 x^2 + 5 x from both sides:
x - 3 x^2 = 0
Factor x and constant terms from the left hand side:
-(x (3 x - 1)) = 0
Multiply both sides by -1:
x (3 x - 1) = 0
Split into two equations:
x = 0 or 3 x - 1 = 0
Add 1 to both sides:
x = 0 or 3 x = 1
Divide both sides by 3:
x = 0 or x = 1/3
4 + 2/x ⇒ 2/0 + 4 = ∞^~
5 + 5/(3 x) ⇒ 5/(3 0) + 5 = ∞^~:
So this solution is incorrect
4 + 2/x ⇒ 4 + 2/(1/3) = 10
5 + 5/(3 x) ⇒ 5 + 5/(3/3) = 10:
So this solution is correct
The solution is: x = 1/3
+2446 Upon further review, there appears to be ambiguity because the interpretations of 2/x+4=5/3x+5 are different.
ProMagma solved the equation \(\frac{2}{x}+4=\frac{5}{3}x+5\)
Guest solved the equation \(\frac{2}{x}+4=\frac{5}{3x}+5\)
This discrepancy occurs at the right side of the equation. That division symbol causes interpretations to differ; there really should be parentheses to clarify. This would not be the first time this forum has seen this issue. Strictly speaking, I believe that ProMagma's interpretation to be correct, but ManuelBautista2019 could have meant the other interpretation.
