Analyzing Solution Sets to Linear Equations with the Variable on Both Sides-
Infinitely many solutions
5x-2x+7-x=__x__
answers 1-9
To analyze the solution set of the equation 5x-2x+7-x=__x__, we can simplify the equation first:
Combining like terms on the left side:
5x - 2x - x + 7 = __x__
(5 - 2 - 1)x + 7 = __x__
2x + 7 = __x__
Now, let's consider the different possibilities for the value of "__x__":
1. If "__x__" represents a specific numerical value:
In this case, the equation 2x + 7 = __x__ would become a regular linear equation. We can solve it by isolating the variable x on one side of the equation. Therefore, it does not represent infinitely many solutions.
2. If "__x__" represents a variable or a parameter:
In this case, the equation 2x + 7 = __x__ would represent a family of linear equations, where each value of "__x__" represents a different equation. This implies that there can be infinitely many solutions since there is more than one equation.
In conclusion, if "__x__" represents a specific numerical value, there will be a single solution. However, if "__x__" represents a variable or a parameter, there will be infinitely many solutions.
To determine the solution set of the given equation 5x - 2x + 7 - x = __x__, we need to simplify it first.
Combining like terms (the terms with the same variable), we have:
5x - 2x - x + 7 = __x__
Simplifying further, we obtain:
2x + 7 = __x__
Now, we can see that the variable "x" is present on both sides of the equation. In such cases, we need to bring all the x terms to one side and all the constant terms to the other side.
Subtracting __x__ from both sides, we get:
2x - __x__ + 7 = 0
Simplifying the equation, we have:
x + 7 = 0
To solve for x, we isolate the variable by moving the constant term to the other side. In this case, we subtract 7 from both sides:
x = -7
Now, let's analyze the solution: x = -7
Since there are no variables left in the equation __x__, the solution is in the form of a constant. In this case, the solution is x = -7.
The equation has a specific solution, which means there is only one unique solution. Hence, there are not infinitely many solutions, rather just one solution, which is x = -7.
In terms of the given list of answers (1-9), the correct answer would be 7, as it matches with the solution x = -7.