$$ x < a \text{ or } x > b $$

$$ a < x < b $$

\begin{align} (2x + 5)(2 - x) & > x^2 - x - 5 \\ 4x - 2x^2 + 10 - 5x & > x^2 - x - 5 \\ -2x^2 - x + 10 & > x^2 - x - 5 \\ -3x^2 + 15 & > 0 \\ 3x^2 - 15 & < 0 \\ x^2 - 5 & < 0 \\ x^2 - (\sqrt{5})^2 & < 0 \\ (x + \sqrt{5})(x - \sqrt{5}) & < 0 \phantom{000000} [a^2 - b^2 = (a + b)(a - b)] \end{align}

$$ - \sqrt{5} < x < \sqrt{5} $$

\begin{align} {1 \over 5}x + 1 & \ge -2 \\ {1 \over 5}x & \ge -3 \\ x & \ge 5(-3) \\ x & \ge -15 \phantom{0000000} [\text{First condition}] \\ \\ \\ 3 - 11x & < 4x^2 \\ 0 & < 4x^2 + 11x - 3 \\ 0 & < (x + 3)(4x - 1) \end{align}

$$ x < -3 \text{ or } x > {1 \over 4} \phantom{0000000} [\text{Second condition}] $$

$$ -15 \le x < -3 \text{ or } x > {1 \over 4} $$

\begin{align*} y & = d^2 - 5d + 80 \\ \\ y & \ge 104 \phantom{00000} [ \text{at least 104 copies}] \\ d^2 - 5d + 80 & \ge 104 \\ d^2 - 5d - 24 & \ge 0 \\ (d + 3)(d - 8) & \ge 0 \end{align*}

\begin{align*} d \le - 3 & \text{ or } d \ge 8 \\ \\ \therefore \text{Least no. of days} & = 8 \end{align*}

\begin{align} x < -2 & \text{ or } x > 5 \\ \\ \implies (x + 2)(x - 5) & > 0 \\ x^2 - 5x + 2x - 10 & > 0 \\ x^2 - 3x - 10 & > 0 \\ x^2 - 3x & > 10 \\ 2(x^2 - 3x) & > 2(10) \\ 2x^2 - 6x & > 20 \phantom{000000} [\text{compare with } ax^2 - bx > 20] \\ \\ \\ \therefore a = 2, b & = 6 \end{align}