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If you were to graph the inequality 35<7x

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.

-5 (x + 5) > - 15, -3 (x - 12) > 0, 1/4 (8x + 16) > - 4, 8x < 4x + 28

1 answer

To address the first part of your question regarding the inequality \( 35 < 7x \):

  1. Open or Closed Circle: You would use an open circle because the inequality does not include equality (it’s a "less than" rather than "less than or equal to").

  2. Arrow Direction: The arrow on the number line would point to the right. This is because you're solving for \( x \) in the inequality; when you manipulate the inequality (by dividing both sides by \( 7 \)), you get \( x > 5 \).

For Question 10, let's analyze the inequalities you've provided to match them with their graphed solutions:

  1. \(-5(x + 5) > -15\):

    • Solving:
      • Distribute: \(-5x - 25 > -15\)
      • Add 25: \(-5x > 10\)
      • Divide by -5 (remember to flip the inequality sign): \(x < -2\)

  2. \(-3(x - 12) > 0\):

    • Solving:
      • Distribute: \(-3x + 36 > 0\)
      • Subtract 36: \(-3x > -36\)
      • Divide by -3 (flip the inequality): \(x < 12\)

  3. \((1/4)(8x + 16) > -4\):

    • Solving:
      • Multiply by 4: \(8x + 16 > -16\)
      • Subtract 16: \(8x > -32\)
      • Divide by 8: \(x > -4\)

  4. \(8x < 4x + 28\):

    • Solving:
      • Subtract \(4x\): \(4x < 28\)
      • Divide by 4: \(x < 7\)

Now we can match the inequalities with their graphs based on the gathered information:

  • \(-5(x + 5) > -15\): Corresponds to \(x < -2\)
  • \(-3(x - 12) > 0\): Corresponds to \(x < 12\)
  • \((1/4)(8x + 16) > -4\): Corresponds to \(x > -4\)
  • \(8x < 4x + 28\): Corresponds to \(x < 7\)

You can match these inequalities with their respective graphs based on the information above!