To simplify the expression [tex]\((12x - 14) - (3x + 9) - (-4 - 1)\)[/tex], we will follow a detailed step-by-step process:
1. Distribute the negative signs:
We start with the given expression:
[tex]\[
(12x - 14) - (3x + 9) - (-4 - 1)
\][/tex]
Distribute the negative sign into the parentheses:
[tex]\[
(12x - 14) - 3x - 9 - (-4 - 1)
\][/tex]
Notice that subtracting a negative is the same as adding a positive, so:
[tex]\[
(12x - 14) - 3x - 9 + 4 + 1
\][/tex]
2. Combine like terms:
Group the terms involving [tex]\(x\)[/tex] together and the constant terms together:
[tex]\[
12x - 3x - 14 - 9 + 4 + 1
\][/tex]
Combine the [tex]\(x\)[/tex] terms first:
[tex]\[
(12x - 3x) - 14 - 9 + 4 + 1 = 9x - 14 - 9 + 4 + 1
\][/tex]
Next, combine the constant terms:
[tex]\[
-14 - 9 + 4 + 1 = -23 + 4 + 1
\][/tex]
Simplify further:
[tex]\[
-23 + 4 = -19
\][/tex]
[tex]\[
-19 + 1 = -18
\][/tex]
3. Finalize the expression:
Combining the simplified terms, we get:
[tex]\[
9x - 18
\][/tex]
Therefore, the simplified expression is:
[tex]\(
9x - 18
\)[/tex]
The answer is [tex]\( \boxed{A \, 9x - 18} \)[/tex].
