Question

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

{3,−8}
left brace 3 comma negative 8 right brace

{x|x>3}
left brace x vertical bar x greater than 3 right brace

The solution set is null.
The solution set is null.

{x|x>−8}

Answer 1

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

1. **Solve \(4x - 3 > 9\)**:
\[
4x - 3 > 9
\]
Add 3 to both sides:
\[
4x > 12
\]
Divide by 4:
\[
x > 3
\]

2. **Solve \(x + 6 > -2\)**:
\[
x + 6 > -2
\]
Subtract 6 from both sides:
\[
x > -8
\]

Now, we combine the solutions:
- The first inequality gives us \(x > 3\).
- The second inequality gives us \(x > -8\).

Since \(x > 3\) is the stricter condition, the solution set for the combined inequalities is:
\[
\{x \mid x > 3\}
\]

So, the correct response is:
\(\{x \mid x > 3\}\) (left brace x vertical bar x greater than 3 right brace).