Determine the value of x satisfying |3x - 2| >= 7.

For an inequality of the form $|A| \ge B$, we have $A \ge B$ or $A \le -B$.

$$3x - 2 \ge 7 \quad \text{or} \quad 3x - 2 \le -7$$

$$3x - 2 \ge 7$$ $$3x \ge 7 + 2$$ $$3x \ge 9$$ $$x \ge \frac{9}{3}$$ $$x \ge 3$$

$$3x - 2 \le -7$$ $$3x \le -7 + 2$$ $$3x \le -5$$ $$x \le -\frac{5}{3}$$

The solution is the union of these two intervals.

$$\boxed{x \le -\frac{5}{3} \quad \text{or} \quad x \ge 3}$$

For an inequality of the form $|A| > B$, we have $A > B$ or $A < -B$.

$$x - 1 > 5 \quad \text{or} \quad x - 1 < -5$$

$$x - 1 > 5$$ $$x > 5 + 1$$ $$x > 6$$

$$x - 1 < -5$$ $$x < -5 + 1$$ $$x < -4$$

The solution is the union of these two intervals.

$$\boxed{x < -4 \quad \text{or} \quad x > 6}$$

For an inequality of the form $|A| \ge B$, we have $A \ge B$ or $A \le -B$.

$$x + 3 \ge 7 \quad \text{or} \quad x + 3 \le -7$$

$$x + 3 \ge 7$$ $$x \ge 7 - 3$$ $$x \ge 4$$

$$x + 3 \le -7$$ $$x \le -7 - 3$$ $$x \le -10$$

The solution is the union of these two intervals.

$$\boxed{x \le -10 \quad \text{or} \quad x \ge 4}$$

For an equation of the form $|A| = B$, we have $A = B$ or $A = -B$.

$$x + 3 = 4 \quad \text{or} \quad x + 3 = -4$$

$$x + 3 = 4$$ $$x = 4 - 3$$ $$x = 1$$

$$x + 3 = -4$$ $$x = -4 - 3$$ $$x = -7$$

The solutions are the two values of $x$.

$$\boxed{x = 1 \quad \text{or} \quad x = -7}$$