Question

Solve the inequality. |2k + 1| ≥ 5

Answer 1

If you remove the absolute value of |2k+1| ≥ 5, you will get:

a) 2k+1 ≥ 5  and b) 2k+1≤ - 5. (for the negative , you flip the inequality sign)
Hence

a) 2k+1 ≥ 52  →  k≥5-1  and k≥ 2  And
b) 2k+1 ≤ - 5  → k≤ - 5- 1 and k ≤ - 3

Then     -3 ≥  k ≥ 2