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So the inequality becomes:rac{-3x + 11}{x - 2} < 0.We analyze the sign of this rational expression by identifying the critical points where the numerator or denominator is zero:Numerator zero: $ -3x + 11 = 0 \Rightarrow x = rac{11}{3} $.Denominator zero: $ x - 2 = 0 \Rightarrow x = 2 $.These divide the real line into intervals:We test the sign of $ rac{-3x + 11}{x - 2} $ in each interval:For $ x < 2 $, say $ x = 0 $: numerator $ -3(0) + 11 = 11 > 0 $, denominator $ 0 - 2 = -2 < 0 $ → negative.For $ 2 < x < rac{11}{3} $, say $ x = 3 $: numerator $ -9 + 11 = 2 > 0 $, denominator $ 1 > 0 $ → positive.For $ x > rac{11}{3} $, say $ x = 4 $: numerator $ -12 + 11 = -1 < 0 $, denominator $ 2 > 0 $ → negative.