Printable math worksheet for writing inequalities from number line graphs.

To solve the problem of writing inequalities that best describe each graph, we need to analyze the number line for each graph and determine the direction of the inequality, the boundary point, and whether the boundary point is included or excluded.

General Guidelines:

1. Direction of the Arrow:
- If the arrow points to the right, the inequality involves \( > \) or \( \geq \).
- If the arrow points to the left, the inequality involves \( < \) or \( \leq \).

2. Boundary Point:
- The boundary point is the specific number on the number line where the shading starts or stops.
- If the boundary point is filled in (closed circle), it means the point is included (\( \geq \) or \( \leq \)).
- If the boundary point is not filled in (open circle), it means the point is excluded (\( > \) or \( < \)).

Solutions:

#### 1)
- Graph: The arrow points to the right, starting from 3 with an open circle at 3.
- Inequality: \( x > 3 \)

#### 2)
- Graph: The arrow points to the left, starting from 0 with a closed circle at 0.
- Inequality: \( x \leq 0 \)

#### 3)
- Graph: The arrow points to the right, starting from -8 with a closed circle at -8.
- Inequality: \( x \geq -8 \)

#### 4)
- Graph: The arrow points to the right, starting from -2 with an open circle at -2.
- Inequality: \( x > -2 \)

#### 5)
- Graph: The arrow points to the left, starting from 10 with an open circle at 10.
- Inequality: \( x < 10 \)

#### 6)
- Graph: The arrow points to the right, starting from -18 with a closed circle at -18.
- Inequality: \( x \geq -18 \)

#### 7)
- Graph: The arrow points to the left, starting from 9 with a closed circle at 9.
- Inequality: \( x \leq 9 \)

#### 8)
- Graph: The arrow points to the right, starting from 0 with an open circle at 0.
- Inequality: \( x > 0 \)

#### 9)
- Graph: The arrow points to the left, starting from 12 with a closed circle at 12.
- Inequality: \( x \leq 12 \)

#### 10)
- Graph: The arrow points to the right, starting from -1 with a closed circle at -1.
- Inequality: \( x \geq -1 \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & x > 3 \\
2) & x \leq 0 \\
3) & x \geq -8 \\
4) & x > -2 \\
5) & x < 10 \\
6) & x \geq -18 \\
7) & x \leq 9 \\
8) & x > 0 \\
9) & x \leq 12 \\
10) & x \geq -1 \\
\end{array}
}
\]