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

Question

ax+c1=bx+c2
(3 points)
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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

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Answer 1

Here are the matches for the one variable equation \( ax + c_1 = bx + c_2 \):

1. The number of x's on both sides of the equation is different (a ≠ b):

   • Number of Solutions: 1 solution (assuming \( a \neq b \), the equation can be solved for 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):

   • Number of Solutions: No solution (the equation simplifies to a contradiction).

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):

   • Number of Solutions: Infinitely many solutions (the equation is always true for all values of x).

Please insert these responses in the corresponding input fields for the question.