Question

Solve the inequality.

|2k + 1| ≥ 5








k ≤ −3 or k ≥ 2


k ≤ −2 or k ≥ 3


k ≥ −3 or k ≥ 2


k ≤ 3 or k​ ≥ −2

Answer 1

To solve the inequality \( |2k + 1| \geq 5 \), we need to consider the two cases that arise from the definition of absolute value.

### Case 1:
\[
2k + 1 \geq 5
\]
Subtracting 1 from both sides:
\[
2k \geq 4
\]
Dividing both sides by 2:
\[
k \geq 2
\]

### Case 2:
\[
2k + 1 \leq -5
\]
Subtracting 1 from both sides:
\[
2k \leq -6
\]
Dividing both sides by 2:
\[
k \leq -3
\]

### Combining the results:
From Case 1, we have \( k \geq 2 \).
From Case 2, we have \( k \leq -3 \).

Therefore, the solution to the inequality \( |2k + 1| \geq 5 \) is:
\[
k \leq -3 \quad \text{or} \quad k \geq 2
\]

The correct answer is:
\[
k \leq -3 \text{ or } k \geq 2
\]