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

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

{x|x>3}

Answer 1

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

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

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

Now we have the two solution sets:
- From the first inequality: \(x > 3\)
- From the second inequality: \(x > -8\)

The solution to the compound inequality is the intersection of the two sets. Since \(x > 3\) is a stricter condition than \(x > -8\), the solution set is:

\[
\{x \mid x > 3\}
\]

Thus, the correct response is:

**\(\{x \mid x > 3\}\)**.