To determine which of the given expressions is equivalent to [tex]\( x - 4(3 - 2x) \)[/tex], we'll simplify the expression step-by-step.
1. Start with the original expression:
[tex]\[
x - 4(3 - 2x)
\][/tex]
2. Distribute the [tex]\(-4\)[/tex] across the terms inside the parentheses:
[tex]\[
x - 4 \cdot 3 + 4 \cdot 2x
\][/tex]
3. Simplify the multiplication:
[tex]\[
x - 12 + 8x
\][/tex]
4. Combine the like terms [tex]\(x\)[/tex] and [tex]\(8x\)[/tex]:
[tex]\[
x + 8x - 12
\][/tex]
[tex]\[
9x - 12
\][/tex]
So, the simplified expression is [tex]\(9x - 12\)[/tex].
5. Let's check against the provided options to find the equivalent expression:
- [tex]\(-12 + 3x\)[/tex]
- [tex]\(-12 - x\)[/tex]
- [tex]\(-12 - 7x\)[/tex]
- [tex]\(-12 + 9x\)[/tex]
The simplified expression [tex]\( 9x - 12 \)[/tex] matches with the fourth option when we rearrange it in the same form:
[tex]\[
-12 + 9x
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{-12 + 9x}
\][/tex]
