Question

14. If you were to graph the inequality 35<7x
on a number line:(2 points)
Would you use an open or closed circle?
open

Would your arrow on the number line point to the left or to the right?
right

Answer 1

Let's break down the inequality \( 35 < 7x \).

1. **Solving the Inequality:**
To find the solution, we can isolate \( x \):
\[
35 < 7x
\]
Divide both sides by 7 (noting that since we are dividing by a positive number, the direction of the inequality stays the same):
\[
\frac{35}{7} < x
\]
Simplifying gives:
\[
5 < x
\]
which can be rewritten as:
\[
x > 5
\]

2. **Graphing the Inequality:**
- **Open or Closed Circle:** Since the inequality is strictly greater than ( \( x > 5 \) ) and does not include 5, you would use an **open circle** at 5.
- **Arrow Direction:** Since \( x \) is greater than 5, the arrow on the number line would point to the **right**.

So your answers are correct:
- **Open circle:** Yes
- **Arrow direction:** Right

The graph would represent all numbers greater than 5, not including 5 itself.