# Solve the equation sin pi(2x-3)/6=-0.5. Write the smallest positive root for your answer.

Solve the equation $\mathrm{sin}\pi \left(2x-3\right)/6=-0.5$. Write the smallest positive root for your answer.
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Marie Horn
$\mathrm{sin}\pi \left(2x-3\right)/6=-0,5$
$\pi \left(2x-3\right)/6=-\pi /6+2\pi nU\pi \left(2x-3\right)/6=-5\pi /6+2\pi n$
$2x-3=-1+12nU2x-3=-5+12n$
$2x=2+12nU2x=-2+12n$
$x=1+6n,n\in zUx=-1+6n,n\in z$
Ответ х=1