Question

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

{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

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

{3,−8}

Answer 1

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

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

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

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

The solution set that satisfies both of these inequalities is the more restrictive one, which is \(x > 3\).

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

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