+0

+2
100
7
+233

solve this equation

2/x+4=5/3x+5

ManuelBautista2019  Nov 10, 2017
Sort:

#1
+548
0

Here is the answer, but all of the work may take a little to type in.

ProMagma  Nov 10, 2017
#2
0

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

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

Guest Nov 10, 2017
#3
+548
-1

Are you sure?

ProMagma  Nov 10, 2017
edited by ProMagma  Nov 10, 2017
#4
+548
0

I thought I got it, but he has a lot more evidence...

ProMagma  Nov 10, 2017
#5
+1602
+2

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.

TheXSquaredFactor  Nov 10, 2017
#7
+548
0

Thank You :)

ProMagma  Nov 12, 2017
#6
+233
0

Thank you Promagna, Guest, XSquaredFactor

ManuelBautista2019  Nov 10, 2017

### 9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details