The diagram shows the curve with equation $$\(y=a \sin (b x)+c\)$$ for $$\(0 \leqslant x \leqslant 2 \pi\)$$, where $$\(a, b\)$$ and $$\(c\)$$ are positive constants. For these values of $$\(a, b\)$$ and $$\(c\)$$, determine the number of solutions in the interval $$\(0 \leqslant x \leqslant 2 \pi\)$$ for each of the following equations: $$\(a \sin (b x)+c=7-x\)$$ ................................................................................................................................................ . ................................................................................................................................................ .

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