Evaluate the expression: 22 - [15 - \48 / (16 - 6 / 3 x 4 - 1)\]

First, perform the division:

$$6 \div 3 = 2$$

Substitute this back:

$$(16 - 2 \times 4 - 1)$$

Next, perform the multiplication:

$$2 \times 4 = 8$$

Substitute this back:

$$(16 - 8 - 1)$$

Finally, perform the subtractions from left to right:

$$16 - 8 = 8$$ $$8 - 1 = 7$$

So, the value inside the parentheses is 7.

$$\{48 \div 7\}$$

This simplifies to $\frac{48}{7}$.

$$[15 - \frac{48}{7}]$$

To subtract, find a common denominator:

$$15 = \frac{15 \times 7}{7} = \frac{105}{7}$$

Now subtract:

$$[\frac{105}{7} - \frac{48}{7}]$$ $$[\frac{105 - 48}{7}]$$ $$[\frac{57}{7}]$$

So, the value inside the square brackets is $\frac{57}{7}$.

$$22 - \frac{57}{7}$$

To subtract, find a common denominator:

$$22 = \frac{22 \times 7}{7} = \frac{154}{7}$$

Now subtract:

$$\frac{154}{7} - \frac{57}{7}$$ $$\frac{154 - 57}{7}$$ $$\frac{97}{7}$$