Question
Q19 The solution to the inequality 3x - 2 < 7 is x < 3. Use set notation to express the values of x that make the inequality 3x - 2 < 7 true.
Answers
GPT-4o mini
To solve the inequality \(3x - 2 < 7\), we can follow these steps:
1. Add 2 to both sides:
\[
3x < 9
\]
2. Divide both sides by 3:
\[
x < 3
\]
Now, in set notation, we express the values of \(x\) that satisfy this inequality. The solution is represented as:
\[
\{ x \in \mathbb{R} : x < 3 \}
\]
This means the set of all real numbers \(x\) such that \(x\) is less than 3.
1. Add 2 to both sides:
\[
3x < 9
\]
2. Divide both sides by 3:
\[
x < 3
\]
Now, in set notation, we express the values of \(x\) that satisfy this inequality. The solution is represented as:
\[
\{ x \in \mathbb{R} : x < 3 \}
\]
This means the set of all real numbers \(x\) such that \(x\) is less than 3.