Question

Ellen's math homework involves finding out how many solutions some equations have. Drag each equation on the left to the number of solutions it has. Choices

A. 5x+1=25
B. 12+3x+5=x+19+2x-2
C. 4x=3x+4-8
D. 2x+10+6x=8x-7
a. No Solution
b. Exactly one Solution
c. Infinitely many Solution

Answer 1

Each equation can have no solution, exactly one solution, or infinitely many solutions. Upon simplifying and solving the equations, A has exactly one solution, B has infinitely many solutions, C has exactly one solution, and D has no solution.

Step-by-step explanation:

Let's analyze each equation:

1. A. 5x + 1 = 25: This is a linear equation with one variable. Subtract 1 from both sides to get 5x = 24, and then divide both sides by 5 to find x = 24/5. Hence, this equation has exactly one solution.
2. B. 12 + 3x + 5 = x + 19 + 2x - 2: First, simplify both sides of the equation by combining like terms. You will get 3x + 17 = 3x + 17, which simplifies to 0 = 0. This means the equation is true for all values of x, so it has infinitely many solutions.
3. C. 4x = 3x + 4 - 8: Simplify the right side to get 4x = 3x - 4. Subtract 3x from both sides, resulting in x = -4, giving us exactly one solution.
4. D. 2x + 10 + 6x = 8x - 7: Combine like terms on the left side to get 8x + 10 = 8x - 7. When we subtract 8x from both sides, we get 10 = -7, which is not possible. Therefore, this equation has no solution.