#### Answer

The solution is $\frac{-4}{25}$

#### Work Step by Step

$\frac{5}{4}$y =$\frac{1}{2}$ - $\frac{7}{10}$ Multiply by LCD,20
20$\frac{5}{4}$y =20$\frac{1}{2}$ -20 $\frac{7}{10}$
$\frac{20\times5y}{4}$ =$\frac{20\times1}{2}$ - $\frac{20\times7}{10}$
$\frac{4\times5\times5y}{4}$ =$\frac{2\times10\times1}{2}$ - $\frac{2\times10\times7}{10}$
5$\times$5y =10$\times$1 -2$\times$7
25y=10-14
25y=-4
$\frac{25y}{25}$=$\frac{-4}{25}$
y=$\frac{-4}{25}$
The solution is $\frac{-4}{25}$
Check
Replace y with $\frac{-4}{25}$
$\frac{5}{4}$y =$\frac{1}{2}$ - $\frac{7}{10}$
$\frac{5}{4}$$\times$$\frac{-4}{25}$ =$\frac{1}{2}$ - $\frac{7}{10}$
$\frac{5\times-4}{4\times25}$ =$\frac{1}{2}$ - $\frac{7}{10}$
$\frac{5\times-4}{4\times5\times5}$ =$\frac{1}{2}$ - $\frac{7}{10}$
$\frac{-4}{20}$ =$\frac{1}{2}$ - $\frac{7}{10}$ LCD is 20
20$\frac{-4}{20}$ =20$\frac{1}{2}$ - 20$\frac{7}{10}$
-4=10-2$\times$7-4=10-14
-4=-4