To simplify the expression [tex]\(30 - [11 - (3 - 15)]\)[/tex], we need to evaluate it step by step, starting from the innermost parentheses and working our way outward.
1. Evaluate the innermost expression:
[tex]\[
3 - 15
\][/tex]
Subtracting 15 from 3 gives:
[tex]\[
3 - 15 = -12
\][/tex]
2. Replace the innermost expression with its result:
Now the expression becomes:
[tex]\[
30 - [11 - (-12)]
\][/tex]
3. Evaluate the next expression inside the brackets:
[tex]\[
11 - (-12)
\][/tex]
Subtracting [tex]\(-12\)[/tex] is the same as adding 12:
[tex]\[
11 - (-12) = 11 + 12 = 23
\][/tex]
4. Replace the inner expression with its result:
Now the expression is:
[tex]\[
30 - 23
\][/tex]
5. Finally, evaluate the outer expression:
[tex]\[
30 - 23 = 7
\][/tex]
Thus, the simplified result of the expression [tex]\(30 - [11 - (3 - 15)]\)[/tex] is:
[tex]\[
\boxed{7}
\][/tex]
