Evaluate: (-9) - (-56) ÷ (-14) + (-4) × 7

The correct option is -41.

To evaluate the given arithmetic expression, we must follow the standard order of operations (BODMAS / PEMDAS):

1. Brackets / Parentheses
2. Orders / Exponents
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

The expression to evaluate is:

$(-9)-(-56)÷(-14)+(-4)\times 7$

Step 1: Perform Division
Divide $(-56)$ by $(-14)$. Since dividing a negative number by a negative number yields a positive result:

$(-56)÷(-14)=4$

Now substitute this back into the expression:

$(-9)-4+(-4)\times 7$

Step 2: Perform Multiplication
Multiply $(-4)$ by $7$. Multiplying a negative number by a positive number yields a negative result:

$(-4)\times 7=-28$

Substitute this back into the expression:

$(-9)-4+(-28)$

Step 3: Perform Subtraction and Addition (from left to right)
First, calculate $(-9)-4$:

$-9-4=-13$

Next, add $(-28)$ to $-13$:

$-13+(-28)=-13-28=-41$

Thus, the final value of the expression is -41.