1. The problem involves solving and understanding a system of inequalities with variables $v, w, p, n, \lambda, q, x, m$ arranged vertically. 2. The inequalities given are: $$v - w \leq p - w \leq \frac{x}{q} \leq -n + \lambda$$ $$ (q + 9)e - \frac{q}{s} \leq \frac{x}{q} \leq \lambda$$ $$-m \leq \frac{q}{x} - m \leq \frac{1}{x}$$ 3. To analyze these, we consider each chain of inequalities separately, noting that the middle terms are bounded by the terms on either side. 4. For the first chain: - $v - w \leq p - w$ means $v \leq p$ since subtracting $w$ from both sides preserves inequality. - $p - w \leq \frac{x}{q}$ means $p - w$ is less than or equal to $\frac{x}{q}$. - $\frac{x}{q} \leq -n + \lambda$ bounds $\frac{x}{q}$ above. 5. For the second chain: - $(q + 9)e - \frac{q}{s} \leq \frac{x}{q}$ lower bounds $\frac{x}{q}$. - $\frac{x}{q} \leq \lambda$ upper bounds $\frac{x}{q}$. 6. For the third chain: - $-m \leq \frac{q}{x} - m$ implies $\frac{q}{x} \geq 0$ after adding $m$ to both sides. - $\frac{q}{x} - m \leq \frac{1}{x}$ bounds $\frac{q}{x}$ in relation to $m$ and $\frac{1}{x}$. 7. These inequalities describe ranges and relationships between the variables, which can be graphed as piecewise linear inequalities. 8. Without specific values, the solution is the set of all $(v,w,p,n,\lambda,q,x,m)$ satisfying these inequalities. Final answer: The system defines constraints on the variables as above, describing a feasible region bounded by these inequalities.