Question

Which equation has an infinite number of solutions?

A) 4(x + 8) = 4x +32
B) 4(X + 8) = 2x + 12
C) 4(x + 8) = 4x + 8
D) 4(x + 8) = 4x + 2

Answer 1

The equation A) 4(x + 8) = 4x +32 has an infinite number of solutions because after simplification, it results in a true statement for any value of x.

Step-by-step explanation:

The student is asking which equation has an infinite number of solutions. To determine this, we simplify each option:

1. 4(x + 8) = 4x + 32 simplifies to 4x + 32 = 4x + 32, which is true for all x, so it has an infinite number of solutions.
2. 4(x + 8) = 2x + 12 simplifies to 4x + 32 = 2x + 12, which after rearranging gives 2x = -20, thus only one solution.
3. 4(x + 8) = 4x + 8 simplifies to 4x + 32 = 4x + 8, which after simplifying gives 32 = 8, which is never true, so no solutions.
4. 4(x + 8) = 4x + 2 simplifies to 4x + 32 = 4x + 2, which after simplifying gives 32 = 2, which is never true, so no solutions.

Therefore, the equation with an infinite number of solutions is A) 4(x + 8) = 4x +32.