Question

How many solutions does the following equation have?

-4(x+5) = -4x–20

A) No solutions
B) Exactly one solution
C) Infinitely many solutions

Answer 1

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.