Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+c2
a
x
+
c
1
=
b
x
+
c
2
(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
No SolutionOne SolutionTwo SolutionsThree SolutionsInfinite Solutions
One Solution
What about the other ones
The number of x's on both sides of the equation is different: No Solution
The number of x's is the same on both sides of the equation, and the constant is different: One Solution
The number of x's is the same on both sides of the equation and the constant is also the same: Infinite Solutions
The number of x's on both sides of the equation is different (a≠b) => One Solution
To determine the number of solutions for the given one-variable equation "ax+c1=bx+c2", we need to analyze the equation and compare the coefficients and constants on both sides.
In this equation, "a" represents the coefficient of "x" on the left side, and "b" represents the coefficient of "x" on the right side. Similarly, "c1" and "c2" are constants on the left and right side, respectively.
Now let's go through the given options and match them with the appropriate number of solutions:
1. The number of x's on both sides of the equation is different (a≠b):
This situation implies that the coefficients "a" and "b" are not equal. In such cases, there will be precisely one solution to the equation.
2. The number of x's is the same on both sides of the equation, and the constant is different (a=b, c1≠c2):
In this scenario, even though the coefficients "a" and "b" are equal, the constants "c1" and "c2" are not equal. This type of equation also has a unique solution.
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):
When the coefficients "a" and "b" are equal, as well as the constants "c1" and "c2", the equation has infinite solutions. Any value of "x" will make both sides of the equation equal.
Considering the given options, the equation "ax+c1=bx+c2" would be classified as having:
- No Solution if "a" and "b" are different,
- One Solution if "a" equals "b" but "c1" and "c2" are not equal,
- Infinite Solutions if "a", "b", "c1", and "c2" are all equal.
Therefore, the corresponding option to match the description of the one-variable equation is:
- One Solution