Absolutely, let's break down and verify the given expression step by step to ensure it has been simplified correctly.
### Step-by-Step Solution:
1. Original Expression: The given expression is
[tex]\[
-3m - [2m + (5 - m)] + 7.
\][/tex]
2. Handle the Inner Parentheses: Start with the innermost parentheses [tex]$(5 - m)$[/tex]. Nothing can be simplified inside this set, so we leave it as it is.
[tex]\[
-3m - [2m + (5 - m)] + 7.
\][/tex]
3. Distribute the Brackets: Remove the inner brackets by distributing the negative sign through the expression inside the brackets.
[tex]\[
2m + (5 - m) = 2m + 5 - m = m + 5.
\][/tex]
Therefore, the expression simplifies further to:
[tex]\[
-3m - [m + 5] + 7.
\][/tex]
4. Distribute the Negative Sign: Now, distribute the negative sign through the second set of brackets:
[tex]\[
-3m - m - 5 + 7.
\][/tex]
5. Combine Like Terms: Group all like terms together. Combine the [tex]$m$[/tex] terms and the constant terms separately:
[tex]\[
-3m - m = -4m,
\][/tex]
and
[tex]\[
-5 + 7 = 2.
\][/tex]
Thus, the expression simplifies to:
[tex]\[
-4m + 2.
\][/tex]
6. Final Simplified Expression: Putting it all together:
[tex]\[
-4m + 2 \quad \text{or} \quad 2 - 4m.
\][/tex]
### Conclusion:
After verifying each step without actually simplifying it ourselves initially, we can see that the expression [tex]$-3m - [2m + (5 - m)] + 7$[/tex] has been correctly simplified to [tex]$2 - 4m$[/tex].
