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.

{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 solve the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we will solve each inequality separately and then find their intersection.

**1. Solve the first inequality:**

\[
4x - 3 > 9
\]

Add 3 to both sides:

\[
4x > 12
\]

Divide both sides by 4:

\[
x > 3
\]

**2. Solve the second inequality:**

\[
x + 6 > -2
\]

Subtract 6 from both sides:

\[
x > -8
\]

**3. Combine the solutions:**

The solution sets we have are:

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

The intersection of these two inequalities is the more restrictive one:

Thus, the solution set for the combined inequalities is:

\[
x > 3
\]

This can be expressed in set notation as:

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

Therefore, the correct response is:

\(\{x \mid x > 3\}\) (although this specific option isn't listed in your responses; you may want to present this derived answer).