Simplify (−9) − { (−8) + [24 ÷ (13 − 7)] }

Concept

When an expression contains nested grouping symbols, evaluate from the innermost group outward. Within each group, apply division before addition or subtraction, and preserve the signs of integers.

Application

1. Evaluate the innermost parentheses: 13 − 7 = 6.

2. Perform the division inside the square brackets: 24 ÷ 6 = 4.

3. Evaluate the braces: (−8) + 4 = −4.

4. Complete the outer subtraction: (−9) − (−4) = −9 + 4 = −5.

Cross-check

As an independent sign-distribution check, (−9) − {(−8) + 4} = (−9) + 8 − 4 = −1 − 4 = −5.

Therefore, the simplified value is −5.