The value of $3+2\times [7+(5+7)÷2]\text{ is equal to:}$

The correct answer is 29.

To find the value of the given mathematical expression, we follow the standard order of operations (BODMAS / PEMDAS):

1. Parentheses / Brackets (innermost first)
2. Orders (powers, roots)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

The given expression is:

$3+2\times [7+(5+7)÷2]$

Step 1: Simplify inside the innermost round brackets:

$5+7=12$

Substituting this back into the expression:

$3+2\times [7+12÷2]$

Step 2: Perform the division inside the square brackets:

$12÷2=6$

Substituting this value back into the expression:

$3+2\times [7+6]$

Step 3: Complete the addition inside the square brackets:

$7+6=13$

So the expression simplifies to:

$3+2\times 13$

Step 4: Perform multiplication before addition:

$2\times 13=26$

Step 5: Perform the final addition:

$3+26=29$

Thus, the final simplified value of the expression is 29.