Solve [tex] \frac{1}{5}(2-3y) \ \textless \ -2 [/tex]

A. [tex] y \ \textgreater \ 4 [/tex]
B. [tex] y \ \textgreater \ -4 [/tex]
C. [tex] y \ \textless \ -4 [/tex]
D. [tex] y \ \textless \ 4 [/tex]
E. [tex] y \leq 4 [/tex]



Answer :

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]