1. **State the problem:** Solve the inequality $|2x + 1| \geq 5$. 2. **Recall the definition of absolute value inequality:** For $|A| \geq B$ where $B \geq 0$, the solution is $A \leq -B$ or $A \geq B$. 3. **Apply the rule:** Here, $A = 2x + 1$ and $B = 5$. 4. **Set up two inequalities:** - $2x + 1 \leq -5$ - $2x + 1 \geq 5$ 5. **Solve the first inequality:** - Subtract 1: $2x \leq -6$ - Divide by 2: $x \leq -3$ 6. **Solve the second inequality:** - Subtract 1: $2x \geq 4$ - Divide by 2: $x \geq 2$ 7. **Write the solution:** - $x \leq -3$ or $x \geq 2$ This means the values of $x$ are all numbers less than or equal to $-3$ or greater than or equal to $2$. **Final answer:** $x \leq -3$ or $x \geq 2$