To simplify the expression [tex]\((5a - 2b + c) + (-7a + 9b - 2c)\)[/tex], we need to combine the like terms. Let's go through this step-by-step:
1. Identify the like terms:
- [tex]\(5a\)[/tex] and [tex]\(-7a\)[/tex] are the terms involving [tex]\(a\)[/tex].
- [tex]\(-2b\)[/tex] and [tex]\(9b\)[/tex] are the terms involving [tex]\(b\)[/tex].
- [tex]\(c\)[/tex] and [tex]\(-2c\)[/tex] are the terms involving [tex]\(c\)[/tex].
2. Combine the [tex]\(a\)[/tex] terms:
[tex]\(5a + (-7a) = 5a - 7a = -2a\)[/tex]
3. Combine the [tex]\(b\)[/tex] terms:
[tex]\(-2b + 9b = 9b - 2b = 7b\)[/tex]
4. Combine the [tex]\(c\)[/tex] terms:
[tex]\(c + (-2c) = c - 2c = -c\)[/tex]
Now, we have the simplified expression:
[tex]\[
-2a + 7b - c
\][/tex]
Therefore, the simplified result of [tex]\((5a - 2b + c) + (-7a + 9b - 2c)\)[/tex] is [tex]\(-2a + 7b - c\)[/tex].
