Simplify 35 - [30 + {10 + (12 - 10 - 4)}].

To simplify the expression $35-[30+\{10+(12-10-4)\left\}\right]$, we follow the order of operations (BODMAS/PEMDAS rule), which dictates that we simplify the innermost grouping symbols first.

The grouping symbols used here are:

• Parentheses: $(...)$ (innermost)
• Curly brackets/braces: $\{...\}$ (middle)
• Square brackets: $[...]$ (outermost)

Step 1: Simplify the expression inside the innermost parentheses $(12-10-4)$
Perform the subtractions from left to right:
$12-10=2$
$2-4=-2$
So, the expression inside the parentheses becomes $-2$.

Substitute this back into the main expression:
$35-[30+\{10+(-2)\left\}\right]$
Which simplifies to:
$35-[30+\{10-2\left\}\right]$

Step 2: Simplify the expression inside the curly braces $\{10-2\}$
$10-2=8$

Substitute this back into the expression:
$35-[30+8]$

Step 3: Simplify the expression inside the square brackets $[30+8]$
$30+8=38$

Substitute this back into the expression:
$35-38$

Step 4: Perform the final subtraction
$35-38=-3$

Therefore, the simplified value of the given expression is −3.