1. **State the problem:** We need to evaluate the expressions for k, j, and i given $w=3$, $x=2$, $y=-4$, and $z=-2$. 2. **Recall the expressions:** - $k = w + z(3x - 2y)$ - $j = 20 - 2w^2$ - $i = 2(x^3 - z^2)$ 3. **Evaluate k:** - Calculate inside the parentheses: $3x - 2y = 3 \times 2 - 2 \times (-4) = 6 + 8 = 14$ - Multiply by $z$: $z(3x - 2y) = -2 \times 14 = -28$ - Add $w$: $w + z(3x - 2y) = 3 + (-28) = -25$ 4. **Evaluate j:** - Calculate $w^2$: $3^2 = 9$ - Multiply by 2: $2 \times 9 = 18$ - Subtract from 20: $20 - 18 = 2$ 5. **Evaluate i:** - Calculate $x^3$: $2^3 = 8$ - Calculate $z^2$: $(-2)^2 = 4$ - Subtract: $8 - 4 = 4$ - Multiply by 2: $2 \times 4 = 8$ **Final answers:** - $k = -25$ - $j = 2$ - $i = 8$