Answer
$y\gt9.5$ or $y\lt-6\frac{2}{3}$
Work Step by Step
$\frac{4y+2}{5}-5\gt3\longrightarrow$ using the addition property of inequality, add 5 to each side
$\frac{4y+2}{5}-5+5\gt3+5\longrightarrow$ add
$\frac{4y+2}{5}\gt8\longrightarrow$ using the multiplication property of equality, multiply each side by 5
$\frac{4y+2}{5}\times5\gt8\times5\longrightarrow$ multiply
$4y+2\gt40\longrightarrow$ using the subtraction property of inequality, subtract 2 from each side
$4y+2-2\gt40-2\longrightarrow$ subtract
$4y\gt38\longrightarrow$ using the division property of inequality, divide each side by 4
$4y\div4\gt38\div4\longrightarrow$ divide
$y\gt9.5$
OR
$\frac{4-3y}{6}\gt4\longrightarrow$ using the multiplication property of inequality, multiply each side by 6
$\frac{4-3y}{6}\times6\gt4\times6\longrightarrow$ multiply
$4-3y\gt24\longrightarrow$ using the subtraction property of inequality, subtract 4 from each side
$4-3y-4\gt24-4\longrightarrow$ subtract
$-3y\gt20\longrightarrow$ using the division property of inequality, divide each side by -3; reverse the inequality sign
$-3y\div-3\lt20\div-3\longrightarrow$ divide
$y\lt-6\frac{2}{3}$
