5. Match the description of the one variable equation with the number of solutions it will have.(4 points)

Question

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.
x−7=7−x
3(x+5)=3x+5
10−x=25
2(x+4)=2x+5+3

Answer 1

To match each equation with the number of solutions it will have, let's analyze each one.

1. x - 7 = 7 - x
   Rearranging gives:
   \( x + x = 7 + 7 \)
   \( 2x = 14 \)
   \( x = 7 \)
   Number of solutions: 1

2. 3(x + 5) = 3x + 5
   Simplifying gives:
   \( 3x + 15 = 3x + 5 \)
   Subtracting \( 3x \) from both sides:
   \( 15 = 5 \)
   This is a contradiction.
   Number of solutions: 0 (no solution)

3. 10 - x = 25
   Rearranging gives:
   \( -x = 25 - 10 \)
   \( -x = 15 \)
   \( x = -15 \)
   Number of solutions: 1

4. 2(x + 4) = 2x + 5 + 3
   Simplifying gives:
   \( 2x + 8 = 2x + 8 \)
   Subtracting \( 2x + 8 \) from both sides gives:
   \( 0 = 0 \)
   This is always true, so:
   Number of solutions: Infinite (many solutions)

Now, the matches are as follows:

1. x - 7 = 7 - x => 1 solution
2. 3(x + 5) = 3x + 5 => 0 solutions
3. 10 - x = 25 => 1 solution
4. 2(x + 4) = 2x + 5 + 3 => Infinite solutions (many solutions)

Based on the equations and their solutions, you can fill in the responses accordingly.