To verify that the expression [tex]\(-3m - [2m + (5 - m)] + 7\)[/tex] simplifies correctly to [tex]\(2 - 4m\)[/tex], we can break down the expression step by step and ensure each step matches until we reach the simplified form. Here is a detailed process:
### Step-by-Step Simplification:
1. Original Expression:
[tex]\[
-3m - [2m + (5 - m)] + 7
\][/tex]
2. Expand Inside the Inner Parentheses [tex]\( (5 - m) \)[/tex]:
[tex]\[
-3m - [2m + 5 - m] + 7
\][/tex]
3. Combine Like Terms Inside the Square Brackets:
[tex]\[
2m - m = 1m \rightarrow 2m + 5 - m = m + 5
\][/tex]
Now the expression is:
[tex]\[
-3m - (m + 5) + 7
\][/tex]
4. Distribute the Negative Sign (or Expand) Inside the Square Brackets:
[tex]\[
-3m - m - 5 + 7
\][/tex]
Which simplifies to:
[tex]\[
-3m - m - 5 + 7
\][/tex]
5. Combine Like Terms:
- Combine the [tex]\(m\)[/tex] terms:
[tex]\[
-3m - m = -4m
\][/tex]
- Combine the constants:
[tex]\[
-5 + 7 = 2
\][/tex]
This gives:
[tex]\[
-4m + 2
\][/tex]
6. Final Simplified Expression:
[tex]\[
-4m + 2
\][/tex]
or equivalently:
[tex]\[
2 - 4m
\][/tex]
Thus, through the step-by-step simplification, we observe that the original expression indeed simplifies to [tex]\(2 - 4m\)[/tex]. Each transformation was correctly followed, demonstrating that [tex]\(2 - 4m\)[/tex] is the correct simplified form of the given expression.
