Chapter 4 - Section 4.2 - Compound Inequalities - Exercise Set - Page 273: 67

{$-1,-2,-3$}

Let us consider the first inequality. $5-4x \geq 1 \implies 5-4(-1) \geq 1$ or, $9 \geq 1$ and $5-4(-2) \geq 1$ or, $13 \geq 1$ Now let us consider the second inequality. $3-7x \lt 31 \implies 3-7(-1) \lt 31$ or, $10 \lt 31$ and $3-7(-2) \lt 31$ or, $17 \lt 31$ Also, $3-7(-3) \lt 31$ or, $24 \lt 31$ Our result is: {$-1,-2,-3$}