Find the solution set of 4x−3>94x−3>9 and x+6>−2x+6>−2.(1 point)

To solve the inequalities \(4x - 3 > 9\) and \(x + 6 > -2x + 6\):

1. **Solve the inequality \(4x - 3 > 9\):**

\[
4x - 3 > 9
\]
Add 3 to both sides:
\[
4x > 12
\]
Divide by 4:
\[
x > 3
\]

2. **Solve the inequality \(x + 6 > -2x + 6\):**

\[
x + 6 > -2x + 6
\]
Subtract 6 from both sides:
\[
x > -2x
\]
Add \(2x\) to both sides:
\[
3x > 0
\]
Divide by 3:
\[
x > 0
\]

3. **Combine the solution sets:**

From the first inequality, we have \(x > 3\).
From the second inequality, we have \(x > 0\).

The more restrictive condition is \(x > 3\).

4. **Conclusion:**

The solution set is \( \{ x \mid x > 3 \} \).

Thus, the correct answer is: **{x | x > 3}**.