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Let’s start by simplifying the inequality given:
\frac{1}{2}(2x+3) - \frac{2}{3}(x+1) < 2x \to x+\frac{3}{2} - \frac{2}{3}x - \frac{2}{3} -2x <0 \to \text{multiplying the whole equation with 6}
\to 6x +9 -4x -4 -12x <0 \to -10x +5 <0 \to 5<10x \to x>\frac{1}{2}.
So the correct answer is (A).
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