# Math Help - Equation help

1. ## Equation help

1/3 - x+1/5 = x/3

15(1/3-x/5+1/5) = 15(x/3)

15/3-15x/5+15/5 = 15x/3

5-3x+3=5x

8-3x=5x

8/8=8x/8

x=1

The book gets 1/4

have I made a mistep, Ive done this problem 3 times?

2. Originally Posted by Aristoxenus
1/3 - x+1/5 = x/3
Here is the first mistake: You didn't use brackets! Actually you mean:

1/3 - (x+1)/5 = x/3

Better learn some LaTeX.

15(1/3-x/5+1/5) = 15(x/3)

15/3-15x/5+15/5 = 15x/3

5-3x+3=5x

8-3x=5x

8/8=8x/8

x=1

The book gets 1/4

have I made a mistep, Ive done this problem 3 times?
To multiply through by 15 is the right idea:

$\dfrac13-\dfrac{x+1}5 = \dfrac x3~\buildrel\cdot \rem 15 \over \implies ~ 5-3(x+1)=5x$

Expand the bracket, collect like terms - and you'll get the given result.

3. Thank you