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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.

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

2 number lines: 1, open circle at point 12 going to the left, 2, open circle at -2 going to the left

1 answer

To match the inequalities to their graphed solutions, we will analyze each of the provided inequalities and determine which one corresponds to the given number line graphs.

  1. -3(x - 12) > 0

    • Solving this inequality:
      • Divide by -3 and flip the inequality:
      • So, \(x - 12 < 0\)
      • Therefore, \(x < 12\).
    • This corresponds to an open circle at 12 going to the left.

  2. 1/4(8x + 16) > -4

    • Solving this inequality:
      • Multiply both sides by 4:
      • \(8x + 16 > -16\)
      • Subtract 16 from both sides:
      • \(8x > -32\)
      • Divide by 8:
      • \(x > -4\).
    • This does not directly seem to match either number line.

  3. -5(x + 3) > -15

    • Solving this inequality:
      • Divide by -5 (flip the inequality):
      • So, \(x + 3 < 3\)
      • Subtract 3 from both sides:
      • \(x < 0\).
    • This does not directly seem to match either number line.

  4. 8x < 4x + 28

    • Solving this inequality:
      • Subtract 4x from both sides:
      • \(4x < 28\)
      • Divide by 4:
      • \(x < 7\).
    • This does not directly seem to match either number line.

Now, comparing the number lines:

  • The first number line has an open circle at point 12 and goes to the left, which corresponds to the solution for -3(x - 12) > 0, so it matches with option 1.
  • The second number line has an open circle at -2 and goes to the left. Since none of the simplified inequalities directly correspond with -2, we will check from the approximated inequalities:
  • -5(x + 3) > -15 simplifies to \(x < 0\), which isn't an exact match but it is the closest to match to the left of -2.

Thus, the matching is:

  • -3(x - 12) > 0 matches with the first number line (open circle at point 12).
  • -5(x + 3) > -15 corresponds indirectly to the second number line (open circle at -2).

Final response:

  • For the first number line, choose: -3(x - 12) > 0
  • For the second number line, choose: -5(x + 3) > -15