We need to solve the inequality [tex]\(-6(4-x) \leq -4(x+1)\)[/tex].
1. Expand both sides of the inequality:
[tex]\[
-6(4 - x) \leq -4(x + 1)
\][/tex]
Expanding the left side:
[tex]\[
-6 \cdot 4 + 6x = -24 + 6x
\][/tex]
Expanding the right side:
[tex]\[
-4 \cdot x - 4 \cdot 1 = -4x - 4
\][/tex]
So, the inequality becomes:
[tex]\[
-24 + 6x \leq -4x - 4
\][/tex]
2. Isolate the variable terms on one side:
Add [tex]\(4x\)[/tex] to both sides:
[tex]\[
-24 + 6x + 4x \leq -4 + 4x + 4x
\][/tex]
Simplifying yields:
[tex]\[
-24 + 10x \leq -4
\][/tex]
3. Move the constant term to the other side:
Add 24 to both sides:
[tex]\[
-24 + 24 + 10x \leq -4 + 24
\][/tex]
Simplifying yields:
[tex]\[
10x \leq 20
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 10:
[tex]\[
x \leq 2
\][/tex]
Thus, our solution is [tex]\(x \leq 2\)[/tex].
Therefore, the correct answer is:
C. [tex]\(x \leq 2\)[/tex]
