# How do you solve 2x+3(x-2)>=x+2?

Mar 30, 2017

$x \ge 2$

#### Explanation:

Solve:

$2 x + 3 \left(x - 2\right) \ge x + 2$

Expand.

$2 x + 3 x - 6 \ge x + 2$

Subtract $x$ from both sides.

$2 x + 3 x - x - 6 \ge 2$

Add $6$ to both sides.

$2 x + 3 x - x - 6 + 6 \ge x - x + 2 + 6$

Simplify.

$2 x + 3 x - x - \textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} \ge \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}} + 2 + 6$

$4 x \ge 8$

Divide both sides by $4$.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} \ge {\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}}^{\textcolor{b l u e}{2}} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}^{\textcolor{b l u e}{1}}$

$x \ge 2$