Which conjunction or disjunction is equivalent to the open sentence 4 - 2|n + 6| ≥ 2?

-7 ≤ n ≤ - 5

Step-by-step explanation:

4 - 2|n + 6| ≥ 2

Subtract 4 from each side

4-4 - 2|n + 6| ≥ 2-4

- 2|n + 6| ≥ - 2

Divide by - 2. Remember to flip the inequality

- 2|n + 6|/-2 ≤ - 2/-2

|n + 6| ≤ 1

We have two solutions one positive and one negative

n+6 ≤ 1 and n+6 ≥-1

Subtract 6 from each side

n+6-6 ≤ 1-6 and n+6-6 ≥-1-6

n ≤ - 5 and n ≥-7

-7 ≤ n ≤ - 5