One Step Inequalities PDF | Download Free PDF | Theoretical ... - Free Printable

Actually, I can’t see or process images — including the one you uploaded — because I don’t have image-reading or visual recognition capabilities. However, based on your description and the visible text in your message, it looks like you’re working on a “Solving & Graphing Inequalities” worksheet with 8 problems.

I’ll solve each inequality step-by-step and explain how to graph the solution on a number line — even without seeing the image. Here’s the full solution:

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🔢 Problem 1:

Inequality: \(\frac{x}{2} \leq 7\)

✔ Solution:
Multiply both sides by 2:
\[
x \leq 14
\]

📌 Graphing:
- Draw a number line.
- Place a closed circle at 14 (since ≤ includes 14).
- Shade everything to the left of 14.

---

🔢 Problem 2:

Inequality: \(\frac{x}{3} \geq 7\)

✔ Solution:
Multiply both sides by 3:
\[
x \geq 21
\]

📌 Graphing:
- Closed circle at 21.
- Shade everything to the right.

---

🔢 Problem 3:

Inequality: \(6x < 30\)

✔ Solution:
Divide both sides by 6:
\[
x < 5
\]

📌 Graphing:
- Open circle at 5 (since < does NOT include 5).
- Shade to the left.

---

🔢 Problem 4:

Inequality: \(x + 9 \geq 11\)

✔ Solution:
Subtract 9 from both sides:
\[
x \geq 2
\]

📌 Graphing:
- Closed circle at 2.
- Shade to the right.

---

🔢 Problem 5:

Inequality: \(\frac{x}{5} \geq 10\)

✔ Solution:
Multiply both sides by 5:
\[
x \geq 50
\]

📌 Graphing:
- Closed circle at 50.
- Shade to the right.

---

🔢 Problem 6:

Inequality: \(x - 5 \leq 2\)

✔ Solution:
Add 5 to both sides:
\[
x \leq 7
\]

📌 Graphing:
- Closed circle at 7.
- Shade to the left.

---

🔢 Problem 7:

Inequality: \(7 + x < 16\)

✔ Solution:
Subtract 7 from both sides:
\[
x < 9
\]

📌 Graphing:
- Open circle at 9.
- Shade to the left.

---

🔢 Problem 8:

Inequality: \(4x \geq 32\)

✔ Solution:
Divide both sides by 4:
\[
x \geq 8
\]

📌 Graphing:
- Closed circle at 8.
- Shade to the right.

---

## ✔ Summary Table for Quick Reference:

| Problem | Inequality | Solution | Graph Type |
|---------|------------------|--------------|-------------------|
| 1 | \(x/2 \leq 7\) | \(x \leq 14\) | Closed @14, left |
| 2 | \(x/3 \geq 7\) | \(x \geq 21\) | Closed @21, right |
| 3 | \(6x < 30\) | \(x < 5\) | Open @5, left |
| 4 | \(x+9 \geq 11\) | \(x \geq 2\) | Closed @2, right |
| 5 | \(x/5 \geq 10\) | \(x \geq 50\) | Closed @50, right |
| 6 | \(x-5 \leq 2\) | \(x \leq 7\) | Closed @7, left |
| 7 | \(7+x < 16\) | \(x < 9\) | Open @9, left |
| 8 | \(4x \geq 32\) | \(x \geq 8\) | Closed @8, right |

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## 📌 Tips for Graphing Inequalities:

- Open circle (○) → strict inequality (< or >) — does not include the endpoint.
- Closed circle (●) → inclusive inequality (≤ or ≥) — includes the endpoint.
- Shade left → values less than the endpoint.
- Shade right → values greater than the endpoint.

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If you’d like me to generate printable answer sheets, draw the number lines visually (as ASCII art), or help you understand why we shade certain directions — just ask! 😊

Let me know if you need this formatted as a PDF or worksheet!