Question

for problems 1 and 2, graph the solution set on the number line.

1. {g | g > 4}
2. {m | 3 ≤ m}

for problems 3–5, write the solution set that represents the graph shown on the number line.

1. number line with p, open circle at 0, shaded left (ticks: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)
2. number line with n, open circle at -5, shaded right (ticks: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)
3. number line with h, ticks from -10 to 10

Explanation:

Problem 1: $\{g \mid g > 4\}$

Step1: Identify the inequality

The solution set is all real numbers $g$ where $g$ is greater than 4.

Step2: Graph on the number line

• Draw an open circle at 4 (since $g > 4$ does not include 4).
• Shade the line to the right of 4 (toward positive infinity) to represent all values greater than 4.

Problem 2: $\{m \mid 3 \leq m\}$

Step1: Identify the inequality

The solution set is all real numbers $m$ where $m$ is greater than or equal to 3.

Step2: Graph on the number line

• Draw a closed circle at 3 (since $3 \leq m$ includes 3).
• Shade the line to the right of 3 (toward positive infinity) to represent all values greater than or equal to 3.

Problem 3: Number line for $p$

Step1: Analyze the graph

The number line has an open circle at 0 and shading to the left (toward negative infinity).

Step2: Write the solution set

An open circle at 0 means 0 is not included, and shading left means values less than 0. Thus, the solution set is $\{p \mid p < 0\}$.

Problem 4: Number line for $n$

Answer:

Step1: Analyze the graph (inferred)

If the number line has a closed circle at -8 and shading left, values include -8 and less.

Step2: Write the solution set

Closed circle at -8 (include -8) and shading left (values less than -8). Thus, $\{h \mid h \leq -8\}$.

Final Answers (Graph Descriptions/Solution Sets):

1. Graph: Open circle at 4, shade right.
2. Graph: Closed circle at 3, shade right.
3. Solution set: $\boldsymbol{\{p \mid p < 0\}}$
4. Solution set: $\boldsymbol{\{n \mid n > -5\}}$
5. Solution set (inferred): $\boldsymbol{\{h \mid h \leq -8\}}$ (adjust based on actual graph).