10) \( x^{2}-6 x+9>0 \)

This inequality can be factored into \( (x - 3)^2 > 0 \). The expression \( (x - 3)^2 \) is a perfect square, meaning it is always non-negative, equal to zero only when \( x = 3 \). Therefore, the inequality is satisfied for all \( x \) except \( x = 3 \). So, the solution is \( x < 3 \) or \( x > 3 \). To visualize this, you can think of \( (x - 3)^2 \) as a U-shaped curve that touches the x-axis at \( x = 3 \) but never dips below it. Therefore, the area where this curve is above zero (indicating our inequality holds true) includes all points except that one pesky point where it equals zero! It's like the curve is having a lonely party, and everyone is invited except for the guest of honor!