Question

1. which graph shows the solution of 3n - 1 < 5 and -2n + 3 < 11? (lesson 5-3) a. number line from -5 to 5 with open circles at -4 and 2 b. number line from -5 to 5 with closed circles at -4 and 2 c. number line from -5 to 5 with open circles at -4 and 2, arrows pointing left and right d. number line from -5 to 5 with open circle at 2, arrow pointing left

Explanation:

Step1: Solve \( 3n - 1 < 5 \)

Add 1 to both sides: \( 3n < 5 + 1 \) → \( 3n < 6 \).
Divide by 3: \( n < 2 \).

Step2: Solve \( -2n + 3 < 11 \)

Subtract 3: \( -2n < 11 - 3 \) → \( -2n < 8 \).
Divide by -2 (reverse inequality): \( n > -4 \).

Step3: Analyze the solution \( -4 < n < 2 \)

• Open circles (since \( n

eq -4, 2 \)) at -4 and 2.

• Line between -4 and 2.

Check graphs:

• A: Open circles at -4, 2; line between. Matches \( -4 < n < 2 \).
• B: Closed circles (incorrect, as inequalities are strict).
• C: Arrows outward (incorrect, solution is between -4 and 2).
• D: Arrow left (incorrect, solution has upper bound 2).

Answer:

A. The graph with open circles at -4 and 2, and a line segment between them on the number line from -5 to 5.