Question

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

(1 point)
Responses

{x|x > −8}
{x|x > −8}

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

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

{3, −8}

Answer 1

To find the solution set for the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we will 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 have two solutions:
1. \(x > 3\)
2. \(x > -8\)

The solution set for both inequalities will be the intersection of these solutions. Since \(x > 3\) is a stronger condition (more restrictive) than \(x > -8\), the overall solution set is \(x > 3\).

Thus, the final solution set is:

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

Therefore, the correct response is:

**{x | x > 3}**