Question

If you were to graph the inequality 35 < 7x on a number line:
Would you use an open or closed circle? _______
Would your arrow on the number line point to the left or to the right? ______
Part 1
A. closed
B. open
Part 2
A. left
B. right

Answer 1

To graph the inequality \( 35 < 7x \) on a number line:

1. First, we need to solve for \( x \):

\[
35 < 7x \implies \frac{35}{7} < x \implies 5 < x
\]

This can be rewritten as \( x > 5 \).

2. **For Part 1: Circle Type**
- Since the inequality is strictly greater than (not including 5), you would use an **open circle**.
- Answer: **B. open**

3. **For Part 2: Arrow Direction**
- Because \( x \) is greater than 5, the arrow on the number line would point to the **right**.
- Answer: **B. right**

So, to summarize:
- Part 1: B. open
- Part 2: B. right

Answer 2

are you sure the answer to the question is correct

Answer 3

Yes, the answers provided are correct. Let's review the reasoning step-by-step for clarity.

1. **Solving the Inequality**:
The original inequality given is \( 35 < 7x \). To isolate \( x \):
\[
35 < 7x \implies x > \frac{35}{7} \implies x > 5
\]

2. **Type of Circle**:
Since the inequality is \( x > 5 \), and does not include 5 (it is not \( \geq \)), this means you would use an **open circle** at 5 to represent that the value 5 itself is not included in the solution set.
- **Answer**: **B. open**

3. **Direction of the Arrow**:
Because the inequality indicates that \( x \) is greater than 5, the line will extend to the right from 5, indicating all numbers greater than 5.
- **Answer**: **B. right**

Thus, for the situation described:
- Part 1: **B. open**
- Part 2: **B. right**

This is indeed the correct analysis for graphing the inequality \( 35 < 7x \) on a number line.