# Arithmetic Operation

Algebra Level 4

Consider the arithmetic operations $$\blacktriangle$$ and $$\blacktriangledown$$ defined by $a\blacktriangle b= \begin{cases} a & \text{ if } \lvert a \rvert \geq \lvert b \rvert \\ b & \text{ if } \lvert a \rvert < \lvert b \rvert, \end{cases}$ $a\blacktriangledown b= \begin{cases} a & \text{ if } \lvert a \rvert \leq \lvert b \rvert \\ b & \text{ if } \lvert a \rvert > \lvert b \rvert. \end{cases}$ How many integers $$k$$ are there such that $(-20 \blacktriangle 9) \blacktriangledown (k \blacktriangle 5)=5?$

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