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

This equation will have exactly one solution.

The number of x's is the same on both sides of the equation and the constant is also the same a=b, c^1=c^2

How many solutions?

This equation will have infinitely many solutions.

The number of x's is the same on both sides of the equation, and the constant is different a=b, c1≠c2

How many solutions?

This equation will have no solution.

If the equation has the form ax+c^1=bx+c^2, where a≠b, then it is a one-variable equation with different coefficients for x on both sides. This type of equation will have exactly one solution.

To determine the number of solutions for the equation ax+c^1=bx+c^2, where a≠b, we need to consider the relationship between the coefficients a and b.

In this case, the equation has a single variable, x, and terms involving x on both sides. However, we are given that a and b are not equal (a≠b).

If a and b are not equal, it means that the coefficients of x on both sides of the equation are different. This essentially indicates that the equation has different rates of change on both sides.

So, what does this mean for the number of solutions?

Since the rates of change (the slopes) are different on both sides, the graph of the equation will consist of two distinct lines. These lines will intersect at a point representing the solution to the equation.

Therefore, in this case, the equation ax+c^1=bx+c^2 will have exactly one solution.