Solve the following equation for x Express your answer in the simplest form

-4 (6x-8) = -24x + 32

The equation has

A: no solution

B: Infinitely many solutions

C: one solution ____

1 answer

To solve the equation \(-4(6x - 8) = -24x + 32\), we will first distribute \(-4\) on the left side:

\[ -4 \cdot 6x + (-4) \cdot (-8) = -24x + 32 \]

This simplifies to:

\[ -24x + 32 = -24x + 32 \]

Now, we can observe that the left side and the right side of the equation are identical:

\[ -24x + 32 = -24x + 32 \]

Since both sides of the equation are equal for any value of \(x\), this means that the equation has infinitely many solutions.

Thus, the answer is:

B: Infinitely many solutions.