4) \( \frac{2 x-5}{2 x+1} \geq 0 \quad \) 6) \( \frac{3 x+11}{2+x} \leq 0 \quad \frac{x^{3}-1}{2 x-3 x+1} \pi \) 5) \( \left(x^{2}+6 x-7\right)\left(x^{2}+x+1\right) \geq 0 \) 7) \( \frac{x-11}{4 x-1}<1 \quad-8 \cdot \frac{2 x-7}{3-7 x} \geq 1 \)

Here are the solutions for each inequality: 1. \( \frac{2x - 5}{2x + 1} \geq 0 \): \( x < -\frac{1}{2} \) or \( x \geq \frac{5}{2} \) 2. \( \frac{3x + 11}{2 + x} \leq 0 \): \( -\frac{11}{3} \leq x < -2 \) 3. \( (x^2 + 6x - 7)(x^2 + x + 1) \geq 0 \): \( x \leq -7 \) or \( x \geq 1 \) 4. \( \frac{x - 11}{4x - 1} < 1 \): \( x < -\frac{10}{3} \) or \( x > \frac{1}{4} \) 5. \( -8 \cdot \frac{2x - 7}{3 - 7x} \geq 1 \): \( x < \frac{3}{7} \) or \( x \geq \frac{53}{9} \) These are the ranges of \( x \) that satisfy each inequality.