Question

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

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

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

{3,−8}
left brace 3 comma negative 8 right brace

{x|x>−8}

Answer 1

Let's solve the inequalities one by one.

1. For the inequality \(4x - 3 > 9\):

\[
4x - 3 > 9
\]

Add 3 to both sides:

\[
4x > 12
\]

Now, divide by 4:

\[
x > 3
\]

2. For the inequality \(x + 6 > -2\):

\[
x + 6 > -2
\]

Subtract 6 from both sides:

\[
x > -8
\]

Now, we combine the solutions. We need the values of x that satisfy both inequalities. The more restrictive condition is \(x > 3\).

Thus, the solution set is:

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

So, the correct response is:

\(\{x \,|\, x > 3\}\) (left brace x vertical bar x greater than 3 right brace).