Question

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

{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}
left brace 3 comma negative 8 right brace

{x|x>−8}
left brace x vertical bar x greater than negative 8 right brace

Answer 1

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

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

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

Now we combine the results of both inequalities. The solution set of the combined inequalities is the intersection of the two solutions:

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

The more restrictive condition is \( x > 3 \).

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

So, the correct response is:
**{x|x>3}** (left brace x vertical bar x greater than 3 right brace).