Inequalities Worksheets - Free Printable

To solve the problem of writing inequalities based on the given number lines, we need to carefully analyze each number line and determine the inequality that best describes it. Here's a step-by-step explanation for each part:

---

(1)

- Number Line Description: The arrow points to the right from -3, and there is a closed circle at -3.
- Interpretation: The closed circle at -3 means that -3 is included in the solution set. The arrow pointing to the right indicates all numbers greater than or equal to -3.
- Inequality: \( x \geq -3 \)

---

(2)

- Number Line Description: The arrow points to the left from 4, and there is an open circle at 4.
- Interpretation: The open circle at 4 means that 4 is not included in the solution set. The arrow pointing to the left indicates all numbers less than 4.
- Inequality: \( x < 4 \)

---

(3)

- Number Line Description: The arrow points to the left from -2, and there is a closed circle at -2.
- Interpretation: The closed circle at -2 means that -2 is included in the solution set. The arrow pointing to the left indicates all numbers less than or equal to -2.
- Inequality: \( x \leq -2 \)

---

(4)

- Number Line Description: The arrow points to the right from 0, and there is an open circle at 0.
- Interpretation: The open circle at 0 means that 0 is not included in the solution set. The arrow pointing to the right indicates all numbers greater than 0.
- Inequality: \( x > 0 \)

---

(5)

- Number Line Description: The arrow points to the left from 5, and there is a closed circle at 5.
- Interpretation: The closed circle at 5 means that 5 is included in the solution set. The arrow pointing to the left indicates all numbers less than or equal to 5.
- Inequality: \( x \leq 5 \)

---

(6)

- Number Line Description: The arrow points to the right from -4, and there is an open circle at -4.
- Interpretation: The open circle at -4 means that -4 is not included in the solution set. The arrow pointing to the right indicates all numbers greater than -4.
- Inequality: \( x > -4 \)

---

Final Answer

\[
\boxed{
\begin{array}{ll}
(1) & x \geq -3 \\
(2) & x < 4 \\
(3) & x \leq -2 \\
(4) & x > 0 \\
(5) & x \leq 5 \\
(6) & x > -4 \\
\end{array}
}
\]