11. \( |3 x-4|+2=1 \)

To solve the equation \( |3x - 4| + 2 = 1 \), we first isolate the absolute value by subtracting 2 from both sides: \( |3x - 4| = -1 \). However, since the absolute value can never be negative, there are no solutions to this equation. In short, anytime you find an absolute value expression equaling a negative number, you can quickly conclude that no real number can satisfy that condition! Remember, if you encounter an absolute value equation that leads to a negative result, stop right there—there's no solution! This is a nifty little tip that saves time during problem-solving. Keep it in your back pocket for future challenges!