If $[\sin x] +[\frac{x}{2 π}] + [\frac{2x}{5 π}]= \frac{9x}{10π}$, then the number of solutions in the interval (30, 40) is _____.

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The given equation is valid, if $\frac{9x}{10π}$ is an integer $⇒x=10π,20π,30π, ...$ $⇒x=10π$   $[∵30<x<40]$ Hence, the given equation has only one solution.