14. If you were to graph the inequality 35<7x

Question

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.