Calculate: 5(x-2)-2(x-1) > 4(x+2)

Expression: $5\left( x-2 \right)-2\left( x-1 \right) > 4\left( x+2 \right)$

Distribute $5$ through the parentheses

$5x-10-2\left( x-1 \right) > 4\left( x+2 \right)$

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

$-x > 8+8$

$-x > 16$
\begin{align*}&x < -16 \\&\begin{array} { l }x \in \langle-\infty, -16\rangle\end{array}\end{align*}