Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+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
No solution
One solution
Two solutions
Three solutions
Infinite solutions
One solution
Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+c2
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
One solution
Two solutions
Three solutions
Infinite solutions
No solution
Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+c2
The number of x's on both sides of the equation is different a≠b
No solution
One solution
Two solutions
Three solutions
Infinite solutions
One solution
Match the description of the one variable equation with the number of solutions it will have.
ax+c^1=bx+c^2
The number of x's on both sides of the equation is different a≠b
No solution
One solution
Two solutions
Three solutions
Infinite solutions
One solution
Match the description of the one variable equation with the number of solutions it will have.
ax+c^1=bx+c^2
The number of x's is the same on both sides of the equation, and the constant is different a=b, c^1≠c^2
No solution
One solution
Two solutions
Three solutions
Infinite solutions
One solution
To determine the number of solutions for the given equation, we need to compare the coefficients (a and b) and constants (c1 and c2) on both sides of the equation.
If the coefficients (a and b) are equal, and the constants (c1 and c2) are also equal, then we can simplify the equation to:
ax + c1 = bx + c2
Since the coefficients and constants are the same, the x terms cancel out:
c1 = c2
Now, let's consider the possible scenarios:
1. If the constants (c1 and c2) are equal, then no matter what value x takes, the equation will always hold true. Therefore, the equation in this case will have infinite solutions.
2. If the constants (c1 and c2) are not equal, then the equation will never be true for any value of x, since the left-hand side will not be equal to the right-hand side. In this case, the equation will have no solution.
Hence, the number of solutions for the equation ax + c1 = bx + c2 depends on whether the constants (c1 and c2) are equal or not.
- If c1 = c2, then the equation has infinite solutions.
- If c1 ≠ c2, then the equation has no solution.