Final answer:
Equation A has one solution, equation B has no solution, equation C has one solution, and equation D has infinitely many solutions if B equals 8, otherwise no solution.
Step-by-step explanation:
Let's analyze each of the equations to determine whether they have one solution, infinitely many solutions, or no solution.
- A. 3x = 5: This equation has one solution. It's a simple linear equation with one variable that can be solved by dividing both sides by 3, giving us x = 5/3.
- B. 5x + 7 = 5x - 9: This equation has no solution. If we subtract 5x from both sides, we get 7 = -9, which is not possible. This means there is no value of x that can satisfy the equation.
- C. 7 - 3w = 3: This equation has one solution. It can be simplified to -3w = -4 by subtracting 7 from both sides, and then we can find the solution by dividing both sides by -3, giving us w = 4/3.
- D. Br = r(8): This equation has infinitely many solutions if B equals 8, as we'll get Br = 8r, which is true for any value of r. However, if B is not equal to 8, then the equation has no solution, as no value of r will satisfy Br = 8r.
To summarize, equations A and C each have one unique solution, equation B has no solution, and equation D has either infinitely many solutions or no solution depending on the value of B.