1. **State the problem:** Solve the linear inequality $$-2x + 6 \ge 2$$. 2. **Recall the rule:** When solving inequalities, if you multiply or divide both sides by a negative number, you must reverse the inequality sign. 3. **Isolate the variable term:** Subtract 6 from both sides: $$-2x + 6 - 6 \ge 2 - 6$$ $$-2x \ge -4$$ 4. **Divide both sides by -2:** Since we divide by a negative number, reverse the inequality sign: $$x \le \frac{-4}{-2}$$ $$x \le 2$$ 5. **Final answer:** The solution to the inequality is $$x \le 2$$, meaning all values of $$x$$ less than or equal to 2 satisfy the inequality.