# How do you solve  –2(x – 3) ≥ 5 – (x + 3) ?

Jul 21, 2018

$x \le 4$

#### Explanation:

$- 2 \left(x - 3\right) \ge 5 - \left(x + 3\right)$

Simplify both sides:
$- 2 x + 6 \ge 5 - x - 3$

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

Add $\textcolor{b l u e}{2 x}$ to both sides:
$- 2 x + 6 \quad \textcolor{b l u e}{+ \quad 2 x} \ge 2 - x \quad \textcolor{b l u e}{+ \quad 2 x}$

$6 \ge 2 + x$

Subtract $\textcolor{b l u e}{2}$ from both sides:
$6 \quad \textcolor{b l u e}{- \quad 2} \ge 2 + x \quad \textcolor{b l u e}{- \quad 2}$

$4 \ge x$

Therefore,
$x \le 4$

Hope this helps!