The number of integral solutions $x$ of $\log_{(x+7/2)}\left(\frac{x - 7}{2x - 3}\right)^2 \geq 0$ is _____.
Step-by-Step Solution
Key Concept: Need base $x + 7/2 > 0, \neq 1$; argument $\neq 0$. For base $> 1$ ($x > -5/2$): $|(x - 7)/(2x - 3)| \geq 1 \Rightarrow 3x^2 + 2x - 40 \leq 0 \Rightarrow -4 \leq x \leq 10/3$. Combined: $-5/2 < x \leq 10/3$. Integers: $-2, -1, 0, 1, 2, 3$ (6 values). Base $< 1$ case gives no extra integers. Answer: 6.
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Correct Answer: 6