For each linear equation, indicate whether the equation has no solution, one solution. or infinitely many solutions.
This problem requires you to show your work.
(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(x+2)=5x+16+3x
6x+2−4x=2(x+2)
3(x+3)=7+3x+6−x
8(x+2)=5x+16+3x
First, distribute the 8 on the left side:
8x + 16 = 5x + 16 + 3x
Combine like terms:
8x + 16 = 8x + 16
Subtract 8x from both sides:
16 = 16
This equation has infinitely many solutions.
6x+2−4x=2(x+2)
First, distribute the 2 on the right side:
6x + 2 - 4x = 2x + 4
Combine like terms:
2x + 2 = 2x + 4
Subtract 2x from both sides:
2 = 4
This equation has no solution.
3(x+3)=7+3x+6−x
First, distribute the 3 on the left side:
3x + 9 = 7 + 3x + 6 - x
Combine like terms:
3x + 9 = 9 + 2x
Subtract 2x from both sides:
x + 9 = 9
Subtract 9 from both sides:
x = 0
This equation has one solution: x = 0.