Determine the value of the following mathematical expression:
64 × 2 − (28 + 14) + 45 − 36 + 19 = ?

The correct answer is 114.

To evaluate the given mathematical expression, we follow the order of operations rule (BODMAS/PEMDAS): Parentheses/Brackets first, followed by Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right).

The given expression is:

$64\times 2-(28+14)+45-36+19$

Step 1: Simplify the terms inside the parentheses.
Calculate the sum inside the brackets:

$28+14=42$

Step 2: Perform the multiplication.
Multiply 64 by 2:

$64\times 2=128$

Step 3: Substitute these values back into the main expression.
Rewriting the expression with the simplified terms gives:

$128-42+45-36+19$

Step 4: Perform addition and subtraction from left to right.
Subtract 42 from 128:

$128-42=86$

Add 45 to the result:

$86+45=131$

Subtract 36 from the result:

$131-36=95$

Finally, add 19:

$95+19=114$

Thus, the value of the mathematical expression is 114.