32.2. Find the smallest and largest values of the expression

$$
A=1.5 x+y-z
$$

if $x, y, z$ are non-negative numbers satisfying the system of equations:

$$
\left\{\begin{array}{l}
x-2 y-3 z=-10 \\
x+2 y+z=6
\end{array}\right.
$$

$$
\text { (8-9 grades) }
$$
32.2. Expressing $x$ and $y$ in terms of $z$ from the given system, we get:

$$
x=z-2, \quad y=4-z
$$

Considering that $x \geqslant 0$ and $y \geqslant 0$, i.e., $z-2 \geqslant 0$ and $4-z \geqslant 0$, we arrive at the following relation: $2 \leqslant z \leqslant 4$. Now, substituting the obtained expressions for $x$ and $y$ in terms of $z$ into the expression for $A$:

$$
A=1.5 x+y-z=1.5(z-2)+4-z-z=1-0.5 z
$$

Thus, as $z$ increases, the value of $A$ decreases. Therefore, the minimum value of $A$ will be achieved at the maximum possible value of $z$, i.e., at $z=4$. In this case, $A=-1$. The maximum value of $A$ will be obtained at the minimum value of $z$, i.e., at $z=2$. In this case, $A=0$.