Question

1. select the graph that shows the solution set of $7 \leq n + 5$. (lesson 5-1)

a. \

$$\begin{tikzpicture}>=stealth,scale=0.8 \\draw-> (-6,0) -- (6,0); \\foreach \\x in {-5,-4,-3,-2,-1,0,1,2,3,4,5} \\draw (\\x,0.2) -- (\\x,-0.2) nodebelow {$\\x$}; \\fillblack (2,0) circle (2pt); \\drawthick (2,0) -- (6,0); \\end{tikzpicture}$$

b. \

$$\begin{tikzpicture}>=stealth,scale=0.8 \\draw-> (-6,0) -- (6,0); \\foreach \\x in {-5,-4,-3,-2,-1,0,1,2,3,4,5} \\draw (\\x,0.2) -- (\\x,-0.2) nodebelow {$\\x$}; \\drawthick, dashed (2,0) circle (2pt); \\drawthick (2,0) -- (6,0); \\end{tikzpicture}$$

c. \

$$\begin{tikzpicture}>=stealth,scale=0.8 \\draw-> (-6,0) -- (6,0); \\foreach \\x in {-5,-4,-3,-2,-1,0,1,2,3,4,5} \\draw (\\x,0.2) -- (\\x,-0.2) nodebelow {$\\x$}; \\drawthick, dashed (2,0) circle (2pt); \\drawthick (-6,0) -- (2,0); \\end{tikzpicture}$$

d. \

$$\begin{tikzpicture}>=stealth,scale=0.8 \\draw-> (-6,0) -- (6,0); \\foreach \\x in {-5,-4,-3,-2,-1,0,1,2,3,4,5} \\draw (\\x,0.2) -- (\\x,-0.2) nodebelow {$\\x$}; \\fillblack (2,0) circle (2pt); \\drawthick (-6,0) -- (2,0); \\end{tikzpicture}$$

Explanation:

Step1: Solve the inequality

To solve \(7 \leq n + 5\), subtract 5 from both sides:
\(7 - 5 \leq n + 5 - 5\)
\(2 \leq n\) (or \(n \geq 2\)).

Step2: Analyze the number line graph

• A closed dot (filled circle) on a number line represents inclusion of the point (since \(n \geq 2\), 2 is included).
• The arrow should point to the right (toward larger numbers) because \(n\) is greater than or equal to 2.

Now, check the options:

• Option A: Closed dot at 2, arrow to the right. Matches \(n \geq 2\).
• Option B: Open dot (excludes 2) → Incorrect.
• Option C: Open dot, arrow to the left → Incorrect.
• Option D: Closed dot, arrow to the left → Incorrect.

Answer:

A. The graph with a closed dot at 2 and an arrow pointing to the right (from the number line labeled A with -5 to 5, closed dot at 2, arrow right)