∣π−3∣−∣π−4∣
You asked:
Evaluate the expression: \(\left\lvert \pi - 3\right\rvert - \left\lvert \pi - 4\right\rvert\)
MathBot Answer:
\[\left\lvert \pi - 3\right\rvert - \left\lvert \pi - 4\right\rvert = -7 + 2 \pi \approx -0.71681469282041352307471323344099\]
\[\begin{aligned}\left\lvert \pi - 3\right\rvert - \left\lvert \pi - 4\right\rvert& = \left|{\pi - 3}\right| - \left|{\pi - 4}\right|\\& = \left|{-3 + \pi}\right| - \left|{\pi - 4}\right|\\& = \left(-3 + \pi\right) - \left|{\pi - 4}\right|\\& = \left(-3 + \pi\right) - \left|{-4 + \pi}\right|\\& = \left(-3 + \pi\right) - \left(4 - \pi\right)\\& = -7 + 2 \cdot \pi\end{aligned}\]