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Solve [tex]-6(4-x) \leq -4(x+1)[/tex].

A. [tex]x \leq 3[/tex]
B. [tex]x \geq 3[/tex]
C. [tex]x \leq 2[/tex]
D. [tex]x \geq 2[/tex]

Sagot :

GinnyAnsweridn
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]
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