To simplify the expression [tex]\((4x - 6) - (3x + 6)\)[/tex], let's go through the process step-by-step:
1. Distribute the Negative Sign:
The subtraction sign before the parentheses indicates that each term inside the parentheses should be negated. Therefore,
[tex]\[
(4x - 6) - (3x + 6) = (4x - 6) - 3x - 6.
\][/tex]
2. Combine Like Terms:
Now, group and combine the like terms (terms that contain [tex]\(x\)[/tex] and the constant terms separately):
[tex]\[
4x - 3x - 6 - 6.
\][/tex]
3. Simplify the [tex]\(x\)[/tex]-terms:
Subtract [tex]\(3x\)[/tex] from [tex]\(4x\)[/tex]:
[tex]\[
4x - 3x = x.
\][/tex]
4. Simplify the Constant Terms:
Combine the constant terms [tex]\(-6\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
-6 - 6 = -12.
\][/tex]
5. Write the Final Expression:
Putting the simplified terms together, we get:
[tex]\[
x - 12.
\][/tex]
Therefore, the simplified expression is [tex]\( x - 12 \)[/tex].
So among the given options, the correct answer is:
[tex]\[
x - 12.
\][/tex]
