Question

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

{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

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

{x|x>3}
left brace x vertical bar x greater than 3 right brace

Answer 1

To solve the compound inequalities given, we will solve each inequality separately.

1. For the first inequality:
\[
4x - 3 > 9
\]
We add 3 to both sides:
\[
4x > 12
\]
Now, divide both sides by 4:
\[
x > 3
\]

2. For the second inequality:
\[
x + 6 > -2
\]
We subtract 6 from both sides:
\[
x > -8
\]

Now, combining both inequalities, we are looking for values of \( x \) that satisfy both:
\[
x > 3 \quad \text{and} \quad x > -8
\]

Since \( x > 3 \) is a stricter condition than \( x > -8 \), the solution to the compound inequalities is simply:
\[
x > 3
\]

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

Therefore, the correct response is:
\[
\{x | x > 3\}
\] (left brace x vertical bar x greater than 3 right brace).