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What is [tex]5c - 3d - 12c + d - 6[/tex] written in simplest form?

A) [tex]-9cd - 6[/tex]
B) [tex]-7c + 2d - 6[/tex]
C) [tex]-7c - 2d - 6[/tex]
D) [tex]17c - 4d - 6[/tex]

Answer :

Let's simplify the expression [tex]\(5c - 3d - 12c + d - 6\)[/tex] step by step.

1. Identify and Combine Like Terms:

- For the 'c' terms:
- We have [tex]\(5c\)[/tex] and [tex]\(-12c\)[/tex].
- Combine these by subtracting: [tex]\(5c - 12c = -7c\)[/tex].

- For the 'd' terms:
- We have [tex]\(-3d\)[/tex] and [tex]\(d\)[/tex].
- Combine these: [tex]\(-3d + d = -2d\)[/tex].

2. Constant Term:

- The constant [tex]\(-6\)[/tex] remains unchanged as there are no other constant terms to combine with.

3. Combine Everything:

- Put all the terms together: [tex]\(-7c - 2d - 6\)[/tex].

The expression in its simplest form is [tex]\(-7c - 2d - 6\)[/tex], which corresponds to option C) [tex]\(-7c - 2d - 6\)[/tex].

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