Simplify the following expression:
$84-42+66-(28+22)+35\times 2=?$

The correct answer is 128.

To simplify the given arithmetic expression, we follow the standard order of operations (BODMAS / PEMDAS): Brackets, Orders/Exponents, Division, Multiplication, Addition, and Subtraction.

The given expression is:

$84-42+66-(28+22)+35\times 2$

Step 1: Simplify the terms inside the parentheses (bracket).
Calculate the sum inside the bracket:

$28+22=50$

Step 2: Perform the multiplication.
Multiply the numbers:

$35\times 2=70$

Step 3: Substitute these simplified values back into the expression.
The expression becomes:

$84-42+66-50+70$

Step 4: Perform addition and subtraction sequentially from left to right.

First, subtract 42 from 84:
$84-42=42$

Next, add 66 to 42:
$42+66=108$

Then, subtract 50 from 108:
$108-50=58$

Finally, add 70 to 58:
$58+70=128$

Thus, the final simplified value of the given expression is 128.