Question
Use set notation to express the values of y that make the inequality 4y + 1 > 17 true
Answers
GPT-4o mini
To solve the inequality \(4y + 1 > 17\), we first isolate \(y\).
1. Subtract 1 from both sides:
\[
4y > 17 - 1
\]
\[
4y > 16
\]
2. Next, divide both sides by 4:
\[
y > \frac{16}{4}
\]
\[
y > 4
\]
In set notation, the values of \(y\) that satisfy the inequality can be expressed as:
\[
\{ y \in \mathbb{R} \,|\, y > 4 \}
\]
This means the set of all real numbers \(y\) such that \(y\) is greater than 4.
1. Subtract 1 from both sides:
\[
4y > 17 - 1
\]
\[
4y > 16
\]
2. Next, divide both sides by 4:
\[
y > \frac{16}{4}
\]
\[
y > 4
\]
In set notation, the values of \(y\) that satisfy the inequality can be expressed as:
\[
\{ y \in \mathbb{R} \,|\, y > 4 \}
\]
This means the set of all real numbers \(y\) such that \(y\) is greater than 4.