Certainly! Let's solve the inequality [tex]\(\frac{1}{5}(2 - 3y) < -2\)[/tex] step by step.
1. Clear the fraction: First, multiply both sides of the inequality by 5 to eliminate the fraction.
[tex]\[
5 \cdot \left( \frac{1}{5}(2 - 3y) \right) < 5 \cdot (-2)
\][/tex]
This simplifies to:
[tex]\[
2 - 3y < -10
\][/tex]
2. Isolate the term with the variable: Subtract 2 from both sides to start isolating [tex]\(y\)[/tex]:
[tex]\[
2 - 2 - 3y < -10 - 2
\][/tex]
This simplifies to:
[tex]\[
-3y < -12
\][/tex]
3. Solve for [tex]\(y\)[/tex]: Divide both sides by -3. Remember, dividing by a negative number reverses the inequality sign:
[tex]\[
\frac{-3y}{-3} > \frac{-12}{-3}
\][/tex]
Simplifying this gives:
[tex]\[
y > 4
\][/tex]
After solving this inequality, we find that [tex]\(y > 4\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{A. \, y > 4}
\][/tex]
