Solve $x + \dfrac{x}{2} + \dfrac{x}{3} < 11$ for real $x$.
A$x < 6$
B$x > 6$
C$x < 11$
D$x < 5$
Answer & Solution
Correct answer: A. $x < 6$
Common denominator: $\dfrac{6x + 3x + 2x}{6} < 11 \Rightarrow \dfrac{11x}{6} < 11 \Rightarrow 11x < 66 \Rightarrow x < 6$.
Verify at $x = 6$: $6 + 3 + 2 = 11$. Equal to RHS — strict $<$ excludes the boundary. So $x < 6$ is correct.
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