Question
The solution set of the inequality 3(b – 4) + 2b > 3 is the set of values of b greater than three. Which set notation correctly expresses the solutions?
Answers
GPT-4o mini
To solve the inequality \( 3(b - 4) + 2b > 3 \), we can first simplify the left side.
1. Distribute \(3\) over \( (b - 4) \):
\[
3b - 12 + 2b > 3
\]
2. Combine like terms:
\[
5b - 12 > 3
\]
3. Add \(12\) to both sides:
\[
5b > 15
\]
4. Divide both sides by \(5\):
\[
b > 3
\]
The solution to the inequality is \( b > 3 \).
In set notation, this can be expressed as:
\[
(3, \infty)
\]
This represents the set of all values of \(b\) that are greater than \(3\).
1. Distribute \(3\) over \( (b - 4) \):
\[
3b - 12 + 2b > 3
\]
2. Combine like terms:
\[
5b - 12 > 3
\]
3. Add \(12\) to both sides:
\[
5b > 15
\]
4. Divide both sides by \(5\):
\[
b > 3
\]
The solution to the inequality is \( b > 3 \).
In set notation, this can be expressed as:
\[
(3, \infty)
\]
This represents the set of all values of \(b\) that are greater than \(3\).