$5x-10-2\left( x-1 \right) > 4\left( x+2 \right)$
Distribute $-2$ through the parentheses$5x-10-2x+2 > 4\left( x+2 \right)$
Distribute $4$ through the parentheses$5x-10-2x+2 > 4x+8$
Collect like terms$3x-10+2 > 4x+8$
Calculate the sum$3x-8 > 4x+8$
Move the variable to the left-hand side and change its sign$3x-8-4x > 8$
Move the constant to the right-hand side and change its sign$3x-4x > 8+8$
Collect like terms$-x > 8+8$
Add the numbers$-x > 16$
Change the signs on both sides of the inequality and flip the inequality sign$\begin{align*}&x < -16 \\&\begin{array} { l }x \in \langle-\infty, -16\rangle\end{array}\end{align*}$