To solve the mathematical expression [tex]\(-27 + (-7) + 46 - (-12)\)[/tex], let's go through it step by step.
1. First, address any double negatives:
- The expression contains [tex]\(-(-12)\)[/tex], which simplifies to [tex]\(12\)[/tex]. So, the expression becomes:
[tex]\[
-27 + (-7) + 46 + 12
\][/tex]
2. Combine the negative numbers first:
- Add [tex]\(-27\)[/tex] and [tex]\(-7\)[/tex]:
[tex]\[
-27 + (-7) = -34
\][/tex]
3. Next, add the remaining positive numbers:
- Add [tex]\(46\)[/tex] and [tex]\(12\)[/tex]:
[tex]\[
46 + 12 = 58
\][/tex]
4. Combine the results from the previous steps (negative and positive sums):
- The remaining expression is:
[tex]\[
-34 + 58
\][/tex]
- Adding these together:
[tex]\[
-34 + 58 = 24
\][/tex]
So, the value of the expression [tex]\(-27 + (-7) + 46 - (-12)\)[/tex] is [tex]\(24\)[/tex].
Thus, the final answer is:
[tex]\[
\boxed{24}
\][/tex]
