The simplified value of 178 - 7 x (3 + 17) + 22 is:

The correct option is 60.

To find the simplified value of the mathematical expression, we must follow the order of operations, often remembered using the acronym BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction):

The given expression is:
$178-7\times (3+17)+22$

Step 1: Simplify the expression inside the brackets first.
Calculate the sum inside the parentheses:
$3+17=20$

Now, substitute this value back into the expression:
$178-7\times 20+22$

Step 2: Perform the multiplication next.
Multiply 7 by 20:
$7\times 20=140$

Substitute this value back into the expression:
$178-140+22$

Step 3: Perform addition and subtraction from left to right.
First, subtract 140 from 178:
$178-140=38$

Now, add 22 to the result:
$38+22=60$

Thus, the simplified value of the expression is 60.