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}
left brace x vertical bar x greater than negative 8 right brace

Answer 1

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

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

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

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

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

Now we have the two inequalities:
- \(x > 3\)
- \(x > -8\)

The solution set is determined by the more restrictive inequality, which is \(x > 3\).

Thus, the final solution set is \( \{x \,|\, x > 3\} \).

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