Question

The solution to the inequality 4y+1>17%0D%0A4%0D%0A𝑦%0D%0A+%0D%0A1%0D%0A>%0D%0A17%0D%0A is y>4%0D%0A𝑦%0D%0A>%0D%0A4%0D%0A. Use set notation to express the values of y that make the inequality 4y+1>17%0D%0A4%0D%0A𝑦%0D%0A+%0D%0A1%0D%0A>%0D%0A17%0D%0A true.

Answer 1

To solve the inequality \( 4y + 1 > 17 \), we can follow these steps:

1. Subtract 1 from both sides:
\[
4y > 17 - 1
\]
\[
4y > 16
\]

2. Divide both sides by 4:
\[
y > \frac{16}{4}
\]
\[
y > 4
\]

Now, to express the solution in set notation, we write:
\[
\{ y \in \mathbb{R} \mid y > 4 \}
\]
This means the set of all real numbers \( y \) such that \( y \) is greater than 4.