Question

which number line shows the solutions to ( n < -3 )?
(number lines with -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, some with filled/empty circles and arrows)

Explanation:

Step1: Analyze the inequality \( n < -3 \)

The inequality \( n < -3 \) means we are looking for all numbers less than -3. On a number line, this should be represented by an open circle at -3 (since -3 is not included in the solution, as the inequality is strict, \( < \), not \( \leq \)) and an arrow pointing to the left (towards smaller numbers, i.e., numbers less than -3).

Step2: Evaluate each number line

• First number line: Closed circle at -3 (which would be for \( n \leq -3 \)) and arrow to the right (numbers greater than -3) – incorrect.
• Second number line: Closed circle at -3 (incorrect, as -3 is not included) and arrow to the left – but closed circle is wrong.
• Third number line: Open circle at -3 (correct, since -3 is not included) but arrow to the right (numbers greater than -3) – incorrect.
• Fourth number line: Open circle at -3 (correct, as -3 is not included) and arrow to the left (numbers less than -3) – this matches the inequality \( n < -3 \).

Answer:

The fourth number line (with open circle at -3 and arrow pointing left, labeled with -6 to 6, and the red arrow and markings showing numbers less than -3)