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Match the description of the one variable equation with the number of solutions it will have.

ax+c1=bx+c2(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.
The number of x's on both sides of the equation is different a≠b
The number of x's is the same on both sides of the equation, and the constant is different a=b, c1≠c2
The number of x's is the same on both sides of the equation and the constant is also the same a=b, c1=c2

1 answer

Here are the descriptions matched with the number of solutions for the equation \( ax + c_1 = bx + c_2 \):

  1. The number of x's on both sides of the equation is different (a ≠ b): One solution. (Since you can isolate x)

  2. The number of x's is the same on both sides of the equation, and the constant is different (a = b, c₁ ≠ c₂): No solution. (The equation would imply a false statement)

  3. The number of x's is the same on both sides of the equation and the constant is also the same (a = b, c₁ = c₂): Infinite solutions. (Every value of x will satisfy the equation)

If you need to input these responses, they would be:

  1. One solution
  2. No solution
  3. Infinite solutions