To solve the inequality \( 2 - 3(x - 2) < 2 - 5x \), we first simplify both sides.
Starting with the left side: \[ 2 - 3(x - 2) = 2 - 3x + 6 = 8 - 3x \]
Now the inequality is: \[ 8 - 3x < 2 - 5x \]
Next, we will isolate \( x \). First, we add \( 5x \) to both sides: \[ 8 - 3x + 5x < 2 \] This simplifies to: \[ 8 + 2x < 2 \]
Now, subtract \( 8 \) from both sides: \[ 2x < 2 - 8 \] This simplifies to: \[ 2x < -6 \]
Next, divide both sides by \( 2 \): \[ x < -3 \]
Thus, the truth set of the inequality \( 2 - 3(x - 2) < 2 - 5x \) is: \[ \boxed{(-\infty, -3)} \]