Simplify: $52-\left\{38÷\left(4\times 7-9\right)\right\}$

The correct option is 50.

To simplify the given expression, we follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

The given expression is:

$$52-\left\{38÷\left(4\times 7-9\right)\right\}$$

Step 1: Simplify the innermost parentheses first.
Within the innermost parentheses $\left(4\times 7-9\right)$, we perform the multiplication before the subtraction:

$$4\times 7=28$$

Now, substitute this back into the parentheses and perform the subtraction:

$$28-9=19$$

So, the expression becomes:

$$52-\left\{38÷19\right\}$$

Step 2: Simplify the expression inside the curly braces.
Next, we perform the division inside the curly braces:

$$38÷19=2$$

Now, the expression simplifies to:

$$52-2$$

Step 3: Perform the final subtraction.

$$52-2=50$$

Thus, the simplified value of the expression is 50.