To solve the inequality [tex]\(\frac{1}{3} y > -2\)[/tex], we need to isolate the variable [tex]\(y\)[/tex]. Here is a step-by-step solution:
1. Start with the inequality:
[tex]\[
\frac{1}{3} y > -2
\][/tex]
2. Multiply both sides by 3 to eliminate the fraction. It's important to note that multiplying or dividing both sides of an inequality by a positive number does not reverse the inequality sign. So, we have:
[tex]\[
3 \left( \frac{1}{3} y \right) > 3 (-2)
\][/tex]
3. Simplify both sides:
[tex]\[
y > -6
\][/tex]
Therefore, the solution to the inequality [tex]\(\frac{1}{3} y > -2\)[/tex] is:
[tex]\[
y > -6
\][/tex]
