Question

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

Answer 1

To find the solution set, we need to solve each inequality separately.

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

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

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

\[
x + 6 > -2
\]
Subtract 6 from both sides:
\[
x > -8
\]

Now we combine the solutions:

- From the first inequality, we have \(x > 3\).
- From the second inequality, we have \(x > -8\).

The more restrictive condition is \(x > 3\), since any value greater than 3 will also be greater than -8.

Thus, the solution set is:
\[
\{x | x > 3\}
\]

Therefore, the correct response is:
\(\{x | x > 3\}\).