To solve the equation [tex]\(\frac{1}{3} x = -4\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Identify the fraction and understand its reciprocal: The fraction [tex]\(\frac{1}{3}\)[/tex] implies that [tex]\(x\)[/tex] is being divided by 3. To isolate [tex]\(x\)[/tex], we should multiply both sides of the equation by the reciprocal of [tex]\(\frac{1}{3}\)[/tex], which is 3.
2. Multiply both sides by 3:
[tex]\[
3 \left(\frac{1}{3} x \right) = 3(-4)
\][/tex]
Simplifying both sides, we get:
[tex]\[
x = -12
\][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\frac{1}{3} x = -4\)[/tex] is [tex]\(x = -12\)[/tex].
Therefore, the correct choice is:
- [tex]\(x = -12\)[/tex]
