To solve the inequality [tex]\(-4y + 6 < -14\)[/tex], follow these steps:
1. Subtract 6 from both sides:
[tex]\[
-4y + 6 - 6 < -14 - 6
\][/tex]
Simplifying, we get:
[tex]\[
-4y < -20
\][/tex]
2. Divide both sides by -4:
When you divide both sides of an inequality by a negative number, you need to reverse the inequality sign.
[tex]\[
\frac{-4y}{-4} > \frac{-20}{-4}
\][/tex]
Simplifying, we get:
[tex]\[
y > 5
\][/tex]
Therefore, the solution to the inequality [tex]\(-4y + 6 < -14\)[/tex] is:
[tex]\[
\boxed{y > 5}
\][/tex]
So, the correct answer is [tex]\(\boxed{D. y > 5}\)[/tex].
