Sure! Let's solve the inequality step by step:
Given inequality:
[tex]\[
\frac{1}{3} x < -2
\][/tex]
1. Isolate the Variable:
- To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]. Since [tex]\( x \)[/tex] is currently multiplied by [tex]\(\frac{1}{3}\)[/tex], we can eliminate the fraction by multiplying both sides of the inequality by the reciprocal of [tex]\(\frac{1}{3}\)[/tex], which is 3.
2. Multiply Both Sides by 3:
- Multiplying both sides by 3, we get:
[tex]\[
\frac{1}{3} x \cdot 3 < -2 \cdot 3
\][/tex]
3. Simplify:
- Simplify the left-hand side and the right-hand side of the inequality:
[tex]\[
x < -6
\][/tex]
Therefore, the solution to the inequality [tex]\(\frac{1}{3} x < -2\)[/tex] is:
[tex]\[
x < -6
\][/tex]
This means that [tex]\( x \)[/tex] must be any number less than [tex]\(-6\)[/tex].
