Question

Determine which number(s) make the statement true. Numbers may be used more than once. Desmos Scientific Calculator (To open the calculator in a new window, remember to hold Ctrl before selecting this link.) (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. ___ + 5 = 0 -3 + ___ = negative number ___ - 2 = negative number

Answer 1

Let's analyze each statement one by one to determine which numbers make them true.

1. ___ + 5 = 0

   • To solve for the blank, we subtract 5 from both sides: \[ ___ = 0 - 5 = -5 \] So the answer for this one is -5.

2. -3 + ___ = negative number

   • Let \( x \) represent the blank. We know that -3 is already negative, and any number added to a negative number is negative if that number is not greater than the absolute value of the negative number. Since -3 is negative, it could be any number greater than -3 or could still be a negative number.
   • Therefore, \( x \) could be any number less than or equal to 3 or also a very large negative number. For simplicity, we may use 0 (a neutral number), which fulfills the condition because -3 + 0 = -3 (negative). Other options could include any negative number, but 0 fits clearly.

3. ___ - 2 = negative number

   • Let \( y \) represent the blank. To find the number that fulfills this statement, we need: \[ y - 2 < 0 \] To isolate \( y \), we add 2 to both sides: \[ y < 2 \] Thus, \( y \) should be any number less than 2. A simple example would again be 0.

Putting all the responses together, we can summarize:

1. For the first statement: -5
2. For the second statement: 0 (could also be negative numbers)
3. For the third statement: 0 (or any number less than 2)

You could also further adjust the values of the latter two numbers depending on the requirement to provide diverse numbers or to keep things straightforward.