If you were to graph the inequality 35<7x

Question

on a number line:(2 points)
Would you use an open or closed circle?

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

Question 10
15. Match the inequality to its graphed solution.(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

The option "negative 3 times open paren x minus 12 close paren is greater than 0" (2 of 4) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Options for the response areas: -5 (x + 5) > - 15, -3 (x - 12) > 0, 1/4 (8x + 16) > - 4, 8x < 4x + 28, Open, Closed, Left , RIght

Answer 1

Let's break down the first part of your question regarding the inequality \(35 < 7x\):

1. Would you use an open or closed circle?

   • Since the inequality is strictly less than, \(<\), you would use an open circle on the number line.

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

   • Rearranging the inequality gives \(x > 5\) (since \(35 < 7x\) implies \(x > 5\)). Therefore, you would draw an arrow pointing to the right.

Now for Question 10, let's match the inequality to its graphed solution:

• The inequality \( -3 (x - 12) > 0\) simplifies to \( x < 12\), which would be graphed with an open circle at 12 and an arrow pointing to the left.

Now, let's match the other options:

• Negative 3 times open paren x minus 12 close paren is greater than 0 corresponds to Left (arrow direction).
• The remaining pairs would be:
  • \( -5 (x + 5) > - 15\) would represent \( x < -5\) (Left).
  • \( 1/4 (8x + 16) > - 4 \) simplifies to \( x > -8\) (Right).
  • \( 8x < 4x + 28\) simplifies to \( x < 7\) (Left).

Final Matches:

• Response:
  • -3 (x - 12) > 0 -> Open / Left
  • -5 (x + 5) > - 15 -> Open / Left
  • 1/4 (8x + 16) > - 4 -> Open / Right
  • 8x < 4x + 28 -> Open / Left

Make sure to drag the options into the correct areas on your interface.