Question

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

(1 point)
Responses

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

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

{x|x > −8}
{x|x > −8}

{3, −8}
{3, −8}

Answer 1

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

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

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

Now, we want to find the intersection of \(x > 3\) and \(x > -8\). Since \(x > 3\) is a more restrictive condition, the solution set is:

\[
x > 3
\]

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

So the correct response is:

\(\{x|x > 3\}\)