Reasoning: $\frac{x}{2} = 4\ \ \ \ \Longrightarrow \ \ \ x = 8$

Reasoning: $\frac{x}{3} = 3\ \ \ \Longrightarrow \ \ \ x = 9$

Reasoning: $4x + 1 = 5\ \ \ \ \Longrightarrow \ \ \ \ 4x = 4\ \ \ \ \Longrightarrow \ \ \ x = 1$

Reasoning: $x + 2x = 24\ \ \ \Longrightarrow \ \ \ 3x = 24\ \ \ \ \Longrightarrow \ \ \ x = 8$

Reasoning: $(3x < 15\ \ \ \Longrightarrow \ \ \ x < 5)$

Reasoning: Divide by negative flips sign $\ \ \ \Longrightarrow \ \ \ (x < - \ 3)$

Reasoning: Multiply both sides by $5\ \ \Longrightarrow \ \ (x > 10)$

Reasoning: $x \leq - \ 2$

Reasoning: $2x = 18\ \ \ \ \ \Longrightarrow \ \ \ \ x = 9$

Reasoning: $5x > 15\ \ \ \ \Longrightarrow \ \ \ x > 3$

Reasoning: "$\geq$" includes $3$ and extends right.

Reasoning: $x = 2$

Reasoning: Multiply by $2\ \ \ \ \Longrightarrow \ \ \ x < 10$

Reasoning: Divide by $- \ 3\ \ \ \Longrightarrow$ sign flips $\ \ \ \Longrightarrow \ \ \ x \geq - \ 3$

Reasoning: Constants differ $\Longrightarrow$ contradiction

Reasoning: $\frac{2x\ + \ x}{6} = 5\ \ \ \ \ \Longrightarrow \ \ \frac{3x}{6} = 5\ \ \ \ \ \Longrightarrow \ \ \ \ \ x = 10$

Reasoning: Greater values lie on right side.

Reasoning: $4x \geq 16\ \ \ \ \Longrightarrow \ \ \ \ \ x \geq 4$

Reasoning: $\frac{x}{8} = 2\ \ \ \ \ \Longrightarrow \ \ \ \ x = 16$

Reasoning: "less than or equal to" means $\leq$

Reasoning: $6x < 18\ \ \ \ \Longrightarrow \ \ \ \ x < 3$

Reasoning: "$\geq$" includes boundary and extends right