Question

find the solution set of 4x−3>9and x+6>−2.(1 point)ResponsesThe solution set is null.The solution set is null.{3,−8}left brace 3 comma negative 8 right brace{x|x>−8}left brace x vertical bar x greater than negative 8 right brace{x|x>3}

Answer 1

To find the solution set for the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we'll solve each inequality separately.

1. **Solve the first inequality:**
\[
4x - 3 > 9
\]
Add 3 to both sides:
\[
4x > 12
\]
Now, divide both sides by 4:
\[
x > 3
\]

2. **Solve the second inequality:**
\[
x + 6 > -2
\]
Subtract 6 from both sides:
\[
x > -8
\]

3. **Finding the intersection of the solution sets:**
- The solution set for the first inequality is \(x > 3\).
- The solution set for the second inequality is \(x > -8\).

Now, we take the intersection of these two sets. Since \(x > 3\) is more restrictive than \(x > -8\), the solution to the combined inequalities is:
\[
x > 3
\]

Thus, the solution set in set notation is:
\[
\{ x \mid x > 3 \}
\]

So, the correct response is:
\[
\{ x \mid x > 3 \}
\]