# Solve for: -2(x+4)+2 <= 6x+16

## Expression: $-2\left( x+4 \right)+2 \leq 6x+16$

Distribute $-2$ through the parentheses

$-2x-8+2 \leq 6x+16$

Calculate the sum

$-2x-6 \leq 6x+16$

Move the variable to the left-hand side and change its sign

$-2x-6-6x \leq 16$

Move the constant to the right-hand side and change its sign

$-2x-6x \leq 16+6$

Collect like terms

$-8x \leq 16+6$

$-8x \leq 22$
Divide both sides of the inequality by $-8$ and flip the inequality sign
\begin{align*}&x \geq -\frac{ 11 }{ 4 } \\&\begin{array} { l }\begin{array} { l }\begin{array} { l }x \geq -2 \frac{ 3 }{ 4 },& x \geq -2.75\end{array},& x \in \left[ -\frac{ 11 }{ 4 }, +\infty\right\rangle\end{array}\end{array}\end{align*}