# Fraction issue, I don't know why I'm having this result.

I don't know how to get this result: $\frac{38}{17}$

This is the equation, can anyone explain why?

$(\frac{x}{4}) - (x - \frac{5}{6}) = (1 + \frac{2(x-5)}{3})$

I did this : LCM $= 12$.

Then: $$3(x) - 2(x-5) = 4(1 + 2(x-5)$$

$$3x - 2x + 10 = 4(1 + 2x - 10)$$

$$3x - 2x + 10 = 4 + 8x - 40$$

$$-7x = -46$$

$$\frac{(-46)}{-7}$$

• What steps did you take? Show us what you did, and please read the MathJax tutorial. – Sean Roberson Jun 3 '17 at 15:14
• How would WE know how YOU got your result? – user223391 Jun 3 '17 at 15:15
• Here's a MathJax Tutorial – Sahiba Arora Jun 3 '17 at 15:15
• I can't go to this result, i made in calculator, my results is always different, i did LCM to multiply, but i just can't go to the final result, i don't know why. – Ryan Zagon Jun 3 '17 at 15:16
• $12 \times (x - \frac{5}{6})$ is not equal to $2(x - 5)$. – NickD Jun 3 '17 at 15:24

$$\frac{x}{4} - \left(x - \frac{5}{6}\right) = 1 + \frac{2(x-5)}{3}$$

First add the $x/4$ and $-x$ on the LHS and distribute the $2/3$ on the RHS,

$$\frac{-3}{4}x + \frac{5}{6} = 1 + \frac{2}{3}x - \frac{10}{3}$$

Move all the constants to the LHS and $x$'s to the RHS,

$$\frac{5}{6} - \frac{6}{6} + \frac{20}{6} = \frac{8}{12}x + \frac{9}{12}x$$

Simplify,

$$\frac{19}{6} = \frac{17}{12} x$$

Multiply both sides by $\frac{12}{17}$,

$$\frac{38}{17} = x$$

Hint:

Multiply both sides by 12 to remove all denominators.

Some details:

After multiplication, one gets $$3x-(12x-10)=12+8(x-5)\iff40-12+10=12x-3x+8x.$$

we have $$\frac{x}{4}-x+\frac{5}{6}=1+\frac{2x-10}{3}$$ multipliying by $12$ $$3x-12x+10=12+8x-40$$ $$-9x+10=-28+8x$$ $$-17x=-38$$