To determine whether Trina is correct, we need to simplify both sides of the equation and verify whether they are equal or not:
The given equation is:
\[ -8(x - 4) + 2x = -4(x - 8) - 2x \]
Let's simplify both sides step by step.
Left Side:
\[ -8(x - 4) + 2x \] Distributing \(-8\): \[ -8x + 32 + 2x \] Combining like terms: \[ (-8x + 2x) + 32 = -6x + 32 \] So, the left side simplifies to: \[ -6x + 32 \]
Right Side:
\[ -4(x - 8) - 2x \] Distributing \(-4\): \[ -4x + 32 - 2x \] Combining like terms: \[ (-4x - 2x) + 32 = -6x + 32 \] So, the right side simplifies to: \[ -6x + 32 \]
Now we see that both sides of the equation are: \[ -6x + 32 = -6x + 32 \]
Since both sides are equivalent, the equation does not have exactly one solution; it actually has infinitely many solutions (all values for \(x\) will satisfy the equation).
So, Trina is not correct because the two sides of the equation are equivalent.
The correct answer is: Trina is not correct because the two sides of the equation are equivalent.