To solve the inequality [tex]\(-4y + 6 < -14\)[/tex], let's go through the steps one by one.
1. Write the inequality:
[tex]\[
-4y + 6 < -14
\][/tex]
2. Isolate the term with [tex]\( y \)[/tex]:
Start by subtracting 6 from both sides to remove the constant term on the left-hand side:
[tex]\[
-4y + 6 - 6 < -14 - 6
\][/tex]
Simplifying this, we get:
[tex]\[
-4y < -20
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
Now, we need to isolate [tex]\( y \)[/tex] by dividing both sides of the inequality by [tex]\(-4\)[/tex]. Remember, when we divide or multiply an inequality by a negative number, we must reverse the inequality sign:
[tex]\[
\frac{-4y}{-4} > \frac{-20}{-4}
\][/tex]
Simplifying this, we get:
[tex]\[
y > 5
\][/tex]
4. Write the solution in interval notation:
The solution means that [tex]\( y \)[/tex] must be greater than 5. In interval notation, this is written as:
[tex]\[
(5, \infty)
\][/tex]
Thus, the correct answer to the inequality [tex]\(-4y + 6 < -14\)[/tex] is:
[tex]\[
\boxed{C. \; y > 5}
\][/tex]
