Questions: Solve and graph. [ n+2 leq 8 ] Write the solution using set-builder notation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. n (Simplify your answer. Use integers or fractions for any numbers in the expression. Use one inequality to express your answer if p one inequality that cannot be expressed by a single inequality, separate the inequalities by a comma. Do not include the word 'or' B. The solution set is all real numbers. C. The solution set is the empty set.

Solve and graph.
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n+2 leq 8
]
Write the solution using set-builder notation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. n 
(Simplify your answer. Use integers or fractions for any numbers in the expression. Use one inequality to express your answer if p one inequality that cannot be expressed by a single inequality, separate the inequalities by a comma. Do not include the word 'or'
B. The solution set is all real numbers.
C. The solution set is the empty set.
Transcript text: Solve and graph. \[ |n+2| \leq 8 \] Write the solution using set-builder notation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\{n\}$ $\square$ \} (Simplify your answer. Use integers or fractions for any numbers in the expression. Use one inequality to express your answer if $p$ one inequality that cannot be expressed by a single inequality, separate the inequalities by a comma. Do not include the word 'or' B. The solution set is all real numbers. C. The solution set is the empty set.
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Solution

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Solution Steps

Step 1: Rewrite the absolute value inequality as a compound inequality.

The given inequality is |n + 2| ≤ 8. This is equivalent to -8 ≤ n + 2 ≤ 8.

Step 2: Isolate _n_

Subtract 2 from all parts of the compound inequality: -8 - 2 ≤ n + 2 - 2 ≤ 8 - 2 which simplifies to -10 ≤ n ≤ 6.

Step 3: Write the solution in set-builder notation and select the correct graph

The solution in set-builder notation is {n | -10 ≤ n ≤ 6}. This corresponds to graph D, which shows a line segment from -24 to 0 (and presumably beyond, based on the breaks in the line) and has highlighted endpoints at -10 and 6 connected by a bold line.

Final Answer

{n | -10 ≤ n ≤ 6} and Graph D is the correct graph.

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