Now, determine ALL of the number(s) that will make the statement true. Numbers may be used more than once.

Question

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(3 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.
___ + 8 = 0 -6 + ___ = negative number ___ - (-8) = positive number

Answer 1

To solve the equations and fill in the blanks, let's analyze each statement one by one:

1. ___ + 8 = 0: To make this statement true, we need to find a number \( x \) such that: \[ x + 8 = 0 \] Subtracting 8 from both sides gives us: \[ x = -8 \] So the first blank must be -8.

2. -6 + ___ = negative number: We need to determine a number \( y \) such that when added to -6, the result is still a negative number. For this to happen, \( y \) must be less than 6 (since \(-6 + 6 = 0\), which is not negative). Thus, \( y \) must be any number less than 6.

   So, possible responses for this blank are any number less than 6. Examples include: -7, -10, -1, 0, etc.

3. ___ - (-8) = positive number: This statement simplifies to: \[ z + 8 = \text{positive number} \] For this result to be positive, \( z + 8 > 0 \) must be true, which means: \[ z > -8 \] Thus, the third blank can be any number greater than -8. Examples include: -7, 0, 1, 5, 10, etc.

Summary of the Responses:

• The first blank is -8.
• The second blank can be any number less than 6 (e.g., -7).
• The third blank can be any number greater than -8 (e.g., -7 or 0).

When filling in the blanks, sample responses could be:

1. -8
2. -7 (or any number < 6)
3. 0 (or any number > -8)

Feel free to choose from the examples given for the second and third blanks as applicable.