If you were to graph the inequality 35 < 7x on a number line:

Question

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.