# Thread: Solve the equation:

1. ## Solve the equation:

Solve the equation:
(2/5) + 4/(10x+5) = 7/(2x+1)

I can get it to:
40(x^2) - 270x = -205

The answer the book gives is:
29/4

Help would be appreciated on how to solve this.

Thanks

2. Originally Posted by sstecken
Solve the equation:
$\displaystyle \frac{2}{5} + \frac{4}{10x+5} = \frac{7}{2x+1}$
let's simplify things: $\displaystyle \frac{2}{5} + \frac{4}{5(2x+1)} = \frac{7}{2x+1}$

now let's multiply by $\displaystyle 5(2x+1)$ to get: $\displaystyle \frac{2\cdot 5\cdot (2x+1)}{5} + \frac{4 \cdot 5\cdot (2x+1)}{5(2x+1)} = \frac{7\cdot 5\cdot (2x+1)}{2x+1}$

let's cross things out: $\displaystyle \frac{2\cdot \not 5\cdot (2x+1)}{\not 5} + \frac{4 \cdot \not 5\cdot \rlap{///////}(2x+1)}{\not 5\rlap{///////}(2x+1)} = \frac{7\cdot 5\cdot \rlap{///////}(2x+1)}{\rlap{/////}2x+1}$

so now you have: $\displaystyle 2(2x+1) + 4 = 7\cdot5$

and work it out: $\displaystyle 4x+2 + 4 = 35$

work it out some more: $\displaystyle 4x+6 = 35$

subtract 6: $\displaystyle 4x = 29$

and divide by 4: $\displaystyle \boxed{x = \frac{29}{4}}$