Question

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

Answer 1

-7 ≤ n ≤ -5

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