Question

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

The solution set is null
The solution set is null

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

{3, −8}
{3, −8}

{x | x>−8}

Answer 1

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

1. Solve \(4x - 3 > 9\):

\[
4x - 3 > 9
\]
Add 3 to both sides:

\[
4x > 12
\]
Now, 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 the two solution sets:

- From the first inequality: \(x > 3\)
- From the second inequality: \(x > -8\)

To find the combined solution set, we take the intersection of both conditions. The solution set is:

\[
x > 3
\]

Thus, the correct response is:

**{x | x > 3}**