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.
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.
Solution
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.