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How many integer values of $x$ satisfy $\dfrac{x-1}{3} < \dfrac{5}{7} < \dfrac{x+4}{5}$?

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.