Question

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

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

{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

{x|x>3}
left brace x vertical bar x greater than 3 right brace
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Answer 1

To solve the compound inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we will solve each inequality separately.

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

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

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

The solution set is the intersection of \(x > 3\) and \(x > -8\). Since \(x > 3\) is more restrictive than \(x > -8\), the solution set is simply:

\[
\{x \,|\, x > 3\}
\]

Thus, the correct response is:

\(\{x \,|\, x > 3\}\) (which corresponds to your last option).