Final answer:
The equation -4(x+5) = -4x-20 simplifies to -4x - 20 = -4x - 20. Since both sides of the equation are identical, it has infinitely many solutions (option C).
Step-by-step explanation:
The student asks about the number of solutions for the equation -4(x+5) = -4x–20. To solve for this, we need to simplify and solve the equation:
- Distribute -4 across (x+5), giving -4x - 20.
- On the right side, we simply have -4x - 20 as given in the equation.
- Therefore, the equation simplifies to -4x - 20 = -4x - 20.
As both sides of the equation are identical, every value of x will satisfy the equation. This means that the equation has infinitely many solutions. Therefore, the correct answer is C) Infinitely many solutions.