How do I define absolute value of this exponent function $\sin(e^7) + 7 - 8 \sqrt{2}$

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It's been while since I've studied math. Can someone please explain how to solve the absolute value of this expression without calculator.

$$ \sin(e^7) + 7 - 8 \sqrt{2} $$

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Since $8\sqrt 2>8=7+1\ge 7+\sin e^7$, the number $$\sin e^7+7-8\sqrt 2$$ is negative. Therefore, its absolute value is $$8\sqrt 2-7-\sin e^7$$