Solve the following linear inequalities.

$$4x + 2 - 2 > -6 - 2$$ $$4x > -8$$

$$\frac{4x}{4} > \frac{-8}{4}$$ $$x > -2$$

The solution is $\boxed{x > -2}$.

2. $1 - 2x \le -5$

$$1 - 2x - 1 \le -5 - 1$$ $$-2x \le -6$$

Remember to reverse the inequality sign when dividing by a negative number.

$$\frac{-2x}{-2} \ge \frac{-6}{-2}$$ $$x \ge 3$$

The solution is $\boxed{x \ge 3}$.

3. $\frac{3x+2}{4} \le 2$

$$\frac{3x+2}{4} \times 4 \le 2 \times 4$$ $$3x + 2 \le 8$$

$$3x + 2 - 2 \le 8 - 2$$ $$3x \le 6$$

$$\frac{3x}{3} \le \frac{6}{3}$$ $$x \le 2$$

The solution is $\boxed{x \le 2}$.

4. $\frac{3-2x}{2} > -3$

$$\frac{3-2x}{2} \times 2 > -3 \times 2$$ $$3 - 2x > -6$$

$$3 - 2x - 3 > -6 - 3$$ $$-2x > -9$$

Remember to reverse the inequality sign.

$$\frac{-2x}{-2} < \frac{-9}{-2}$$ $$x < \frac{9}{2}$$

The solution is $\boxed{x < \frac{9}{2}}$.

5. $\frac{1}{2}(x+4) < 3$

$$\frac{1}{2}(x+4) \times 2 < 3 \times 2$$ $$x + 4 < 6$$

$$x + 4 - 4 < 6 - 4$$ $$x < 2$$

The solution is $\boxed{x < 2}$.

6. $3(1-2x) \ge 5$

$$3 \times 1 - 3 \times 2x \ge 5$$ $$3 - 6x \ge 5$$

$$3 - 6x - 3 \ge 5 - 3$$ $$-6x \ge 2$$

Remember to reverse the inequality sign.

$$\frac{-6x}{-6} \le \frac{2}{-6}$$ $$x \le -\frac{1}{3}$$

The solution is $\boxed{x \le -\frac{1}{3}}$.