# Question #09dbc

Sep 26, 2016

start off by writing out
$\frac{3}{2 x - 5} = \frac{7}{3 - 5 x}$

crossmultiply
$\left(3\right) \left(3 - 5 x\right)$
$\left(7\right) \left(2 x - 5\right)$

you now have
$9 - 15 x = 14 x - 35$

combine like terms
-add $35$ to both sides*

you now have
$44 - 15 x = 14 x$

add $15 x$ to both sides to get x on its own side
$44 = 29 x$

$x = \frac{44}{29}$
($1 \frac{15}{29}$ as a mixed fraction)

WORK:
$\frac{3}{2 x - 5} = \frac{7}{3 x - 5}$

$9 x - 15 = 14 x - 35$

$44 - 15 x = 14 x$

$44 = 29 x$

$\frac{44}{29} = x$

TO CHECK, plug in $\frac{44}{29}$ for $x$

*there are different ways of doing this; you could subtract 9 from both sides, you could add 15x to both sides, or you could subtract 14x from both sides