| n + 2 | ≥ 1 please explain it if you can thank you

  (n ≤ -3) ∪ (-1 ≤ n)

Step-by-step explanation:

I like to "unfold" the absolute value expression by copying the right-side expression to the left side (with the same comparison symbol) and negating its value. I do it this way because I find it easier to work the problem "all at once".

  -1 ≥ n +2 ≥ 1

Obviously, -1 ≥ 1 is not true, which means the solution to this inequality will be disjoint sections of the number line. A compound inequality of this nature is generally interpreted to mean the AND of the two inequalities. So, technically, this is an incorrect step. I choose to overlook that, and consider the expression to represent the two inequalities ...

  -1 ≥ n +2 . . . OR

  n +2 ≥ 1

Subtracting 2 from the above compound inequality gives ...

  -3 ≥ n ≥ -1

So, the solution is ...

  (n ≤ -3) ∪ (-1 ≤ n)

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Further explanation

The inequality symbol negates its content if that content is negative. So, the expression ...

  |n+2| ≥ 1

means ...

  ±(n +2) ≥ 1

This resolves to two cases:

  n +2 ≥ 1

and

  -(n +2) ≥ 1

The latter case is equivalent to ...

  n +2 ≤ -1

which can also be written as ...

  -1 ≥ n +2

A more technically correct solution process would identify the two cases and work them separately.

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In the graph, the red shading (with the solid edge) shows the solution with respect to the numbers on the x-axis. If you were to graph this on a number line, you would put solid dots at -3 and -1, and shade the line to their left and right, respectively. The blue curve shows the absolute value, and the green line shows y=1, so you can see that the shaded areas correspond to the absolute value being greater than or equal to 1.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

dalila is incorrect. the whisker on the left is very long, going all the way out to 5. the whisker goes from 5 to 30, so it has a spread of 25. the rest of the box plot values are closer together, so 5 is an outlier