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# can anyone tell me how to solve this absolute-value inequality?

State a conjunction or disjunction equivalent to the open sentence.

4 – 2|n + 6| ≥ 2

Please help me through it I don't understand how to do it.

### 3 Answers

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- Anonymous9 years agoFavorite Answer
1) if n + 6 was positive before absolute-value

4 - 2(n + 6) ≥2

4 - 2n - 12 ≥ 2

4 - 12 - 2 ≥ 2n

-10 ≥ 2n

-5 ≥ n

n ≤ -5

2) if n + 6 was negative before the absolute-value

4 - 2(-1)(n + 6) ≥ 2

4 + 2n + 12 ≥ 2

2n ≥ 2 - 4 - 12

2n ≥ -14

n ≥ -7

Now we are combining both n ≤ -5 and n ≥ -7

All values of n are in between -7 and -5, inclusive.

{all numbers from -7 to -5}

Source(s): I didn't get the conjuction/disjunction part, have you got the question mixed up? - TCLv 79 years ago
4 - 2In + 6I >= 2

- 2In + 6I >= - 2

In+ 6I >= 1

n + 6 >= 1

n >= - 5

- (n + 6) .>= 1

- n - 6 >= 1

- n >= 7

n <= - 7

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