Inequalities - Riverside Math - Free Printable

Problem: Graphing Inequalities on a Number Line Worksheet

The task is to graph the given inequalities on the provided number lines. Below, I will solve each inequality step by step and explain how to graph it.

---

1. \( x < -3 \)

- Inequality: \( x < -3 \)
- Explanation: This means \( x \) is less than \(-3\). On the number line, we shade all numbers to the left of \(-3\).
- Graph:
- Place an open circle at \(-3\) (since \( x \) cannot equal \(-3\)).
- Shade the region to the left of \(-3\).

---

2. \( y > 8 \)

- Inequality: \( y > 8 \)
- Explanation: This means \( y \) is greater than \( 8 \). On the number line, we shade all numbers to the right of \( 8 \).
- Graph:
- Place an open circle at \( 8 \) (since \( y \) cannot equal \( 8 \)).
- Shade the region to the right of \( 8 \).

---

3. \( n \geq 2 \)

- Inequality: \( n \geq 2 \)
- Explanation: This means \( n \) is greater than or equal to \( 2 \). On the number line, we shade all numbers to the right of \( 2 \), including \( 2 \).
- Graph:
- Place a closed circle at \( 2 \) (since \( n \) can equal \( 2 \)).
- Shade the region to the right of \( 2 \).

---

4. \( a \leq 4 \)

- Inequality: \( a \leq 4 \)
- Explanation: This means \( a \) is less than or equal to \( 4 \). On the number line, we shade all numbers to the left of \( 4 \), including \( 4 \).
- Graph:
- Place a closed circle at \( 4 \) (since \( a \) can equal \( 4 \)).
- Shade the region to the left of \( 4 \).

---

5. \( b < -5 \)

- Inequality: \( b < -5 \)
- Explanation: This means \( b \) is less than \(-5\). On the number line, we shade all numbers to the left of \(-5\).
- Graph:
- Place an open circle at \(-5\) (since \( b \) cannot equal \(-5\)).
- Shade the region to the left of \(-5\).

---

6. \( 6 > h \)

- Inequality: \( 6 > h \)
- Explanation: This is equivalent to \( h < 6 \). It means \( h \) is less than \( 6 \). On the number line, we shade all numbers to the left of \( 6 \).
- Graph:
- Place an open circle at \( 6 \) (since \( h \) cannot equal \( 6 \)).
- Shade the region to the left of \( 6 \).

---

7. \( r \geq -6 \)

- Inequality: \( r \geq -6 \)
- Explanation: This means \( r \) is greater than or equal to \(-6\). On the number line, we shade all numbers to the right of \(-6\), including \(-6\).
- Graph:
- Place a closed circle at \(-6\) (since \( r \) can equal \(-6 \)).
- Shade the region to the right of \(-6\).

---

8. \( 0 \leq t \)

- Inequality: \( 0 \leq t \)
- Explanation: This means \( t \) is greater than or equal to \( 0 \). On the number line, we shade all numbers to the right of \( 0 \), including \( 0 \).
- Graph:
- Place a closed circle at \( 0 \) (since \( t \) can equal \( 0 \)).
- Shade the region to the right of \( 0 \).

---

9. \( q \geq -9 \)

- Inequality: \( q \geq -9 \)
- Explanation: This means \( q \) is greater than or equal to \(-9\). On the number line, we shade all numbers to the right of \(-9\), including \(-9\).
- Graph:
- Place a closed circle at \(-9\) (since \( q \) can equal \(-9 \)).
- Shade the region to the right of \(-9\).

---

10. \( 7 > w \)

- Inequality: \( 7 > w \)
- Explanation: This is equivalent to \( w < 7 \). It means \( w \) is less than \( 7 \). On the number line, we shade all numbers to the left of \( 7 \).
- Graph:
- Place an open circle at \( 7 \) (since \( w \) cannot equal \( 7 \)).
- Shade the region to the left of \( 7 \).

---

Final Answer

Each inequality has been graphed as explained above. The key points are:

1. Use a closed circle for \( \leq \) or \( \geq \).
2. Use an open circle for \( < \) or \( > \).
3. Shade the appropriate direction based on the inequality.

\[
\boxed{\text{Graphs as explained above}}
\]