Question

Find the solution set of 4x − 3 > 9 and x + 6 > −2.

(1 point)
Responses

{x|x > 3}
{x|x > 3}

{x|x > −8}
{x|x > −8}

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

{3, −8}

Answer 1

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

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

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

Now we combine the results:
- From the first inequality, we have \( x > 3 \).
- From the second inequality, we have \( x > -8 \).

The solution set that satisfies both inequalities is the intersection of the two solutions:
Since \( x > 3 \) is more restrictive than \( x > -8 \), the solution set is:
\[
\{ x \mid x > 3 \}
\]

So, the correct response is:
**\{x | x > 3\}**.