Domain: $x - 1 > 0 \implies x > 1$.

Inequality (Base $2 > 1$): $x - 1 > 2^4 = 16 \implies x > 17$.

Correct Answer: B. $x > 17$

Domain: $2x + 1 > 0 \implies x > -1/2$.

Inequality (Base $5 > 1$): $2x + 1 \le 5^2 = 25 \implies 2x \le 24 \implies x \le 12$.

Combined: $-1/2 < x \le 12$.

Correct Answer: B. $-1/2 < x \le 12$

Domain: $x + 2 > 0 \implies x > -2$.

Inequality (Base $1/3 < 1$, flip inequality):

Combined: $-2 < x \le 7$.

Correct Answer: B. $-2 < x \le 7$

Domain: $x + 5 > 0 \implies x > -5$.

Inequality (Base $7 > 1$): $x + 5 \ge 12 \implies x \ge 7$.

Correct Answer: A. $x \ge 7$

Domain: $x + 1 > 0 \implies x > -1$, and $3x - 5 > 0 \implies x > 5/3$.

Inequality (Base $2 > 1$): $x + 1 < 3x - 5 \implies 2x > 6 \implies x > 3$.

Combined: $x > 3$.

Correct Answer: C. $x > 3$

Domain: $x^2 > 0 \implies x \ne 0$.

Inequality (Base $9 > 1$): $x^2 > 9^1 = 9 \implies \vert{}x\vert{} > 3 \implies x < -3 \text{ or } x > 3$.

Correct Answer: B. $x < -3 \text{ or } x > 3$

Domain: $x + 2 > 0 \implies x > -2$.

Inequality (Base $3 > 1$): $x + 2 < 27 \implies x < 25$.

Combined: $-2 < x < 25$.

Correct Answer: D. $-2 < x < 25$

Domain: $x^2 - 5 > 0 \implies x < -\sqrt{5} \text{ or } x > \sqrt{5}$.

Inequality (Base $2 > 1$): $x^2 - 5 > 2^2 = 4 \implies x^2 > 9 \implies x < -3 \text{ or } x > 3$.

Correct Answer: A. $x < -3 \text{ or } x > 3$

Domain: $x - 1 > 0 \implies x > 1$, and $2x - 8 > 0 \implies x > 4$.

Inequality (Base $5 > 1$): $x - 1 \ge 2x - 8 \implies x \le 7$.

Combined: $4 < x \le 7$ (matching Option C; option B listed in key corresponds to $x>7$ variant).

Correct Answer: C. $4 < x \le 7$

Domain: $x + 3 > 0 \implies x > -3$, and $7 - x > 0 \implies x < 7$.

Inequality (Base $2 > 1$): $x + 3 > 7 - x \implies 2x > 4 \implies x > 2$.

Combined: $2 < x < 7$.

Correct Answer: A. $2 < x < 7$