To solve the inequality [tex]\( -6(4 - x) \leq -4(x + 1) \)[/tex], we will go through a step-by-step process of simplification and solving.
1. Distribute the constants inside the parentheses:
[tex]\[
-6(4 - x) \leq -4(x + 1)
\][/tex]
Expanding both sides:
[tex]\[
-6 \cdot 4 + 6 \cdot x \leq -4 \cdot x - 4 \cdot 1
\][/tex]
Simplifying further:
[tex]\[
-24 + 6x \leq -4x - 4
\][/tex]
2. Combine the [tex]\(x\)[/tex] terms on one side and constants on the other side:
Add [tex]\(4x\)[/tex] to both sides to get all [tex]\(x\)[/tex] terms on the left:
[tex]\[
-24 + 6x + 4x \leq -4x + 4x - 4
\][/tex]
Simplifying this:
[tex]\[
-24 + 10x \leq -4
\][/tex]
3. Isolate the [tex]\(x\)[/tex] term by eliminating constants from the left side:
Add 24 to both sides:
[tex]\[
-24 + 24 + 10x \leq -4 + 24
\][/tex]
Simplifying this:
[tex]\[
10x \leq 20
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by 10:
[tex]\[
10x \leq 20
\][/tex]
Dividing both sides by 10:
[tex]\[
x \leq \frac{20}{10}
\][/tex]
Simplifying:
[tex]\[
x \leq 2
\][/tex]
Thus, the solution to the inequality [tex]\( -6(4 - x) \leq -4(x + 1) \)[/tex] is [tex]\( x \leq 2 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x \leq 2 \)[/tex]
