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

answer: can and shows the work

step-by-step explanation: