Multiple Select Question
Which equations have infinitely many solutions? Select TWO that apply.
A.
B.
C.
D.
E.
A. 2x + 6 = 3(x + 2)
B. 3x + 5 = 3(x + 1)
C. x + 2 = 2x + 4
D. 4x - 8 = 8(x - 2)
E. 5x + 10 = 2(x + 5)
The options that have infinitely many solutions are A and C.
Explanation:
To have infinitely many solutions, the equations must be identities, meaning both sides of the equation are equal at all times. In options A and C, we can see that every value of x will satisfy the equation and therefore have infinitely many solutions.
To identify which equations have infinitely many solutions, we need to look for equations where the variables cancel out or where the variables have coefficients of zero. However, since the options A, B, C, D, and E are empty, I am unable to provide specific choices in this case. Please provide the equations in order to determine which ones have infinitely many solutions.
To determine which equations have infinitely many solutions, we need to assess the conditions under which an equation would have multiple solutions or infinitely many solutions.
First, it's important to note that multiple solutions refer to a finite number of solutions greater than one, while infinitely many solutions implies an infinite number of solutions.
To identify equations with infinitely many solutions, we need to consider the types of equations that can result in this condition.
Here are a few examples:
1. Linear Equations with Dependent Variables: An equation where the variables are dependent and can be expressed in terms of each other will yield infinitely many solutions. For instance, if you have an equation like 2x - 4y = 0, any point on the line represented by this equation will be a solution.
2. Equations with All Variables Canceling: If you have an equation where all the variables cancel out, you'll also get infinitely many solutions. For example, x + 2 = x + 3. By subtracting 'x' on both sides, we get 2 = 3, which is a contradiction, and this implies that any value of x will satisfy the equation.
In this case, you provided a multiple-select question with five options (A, B, C, D, and E). Since you need to select two options that apply, you should analyze each option to determine if it fits the criteria of equations with infinitely many solutions.
Since there is no information or equations provided in the question, it is not possible to determine the options that have infinitely many solutions. Please provide the equations or additional context for a more accurate selection.