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

{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.

{3,−8}

Answer 1

To solve the inequalities:

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

First, add 3 to both sides:

\[
4x > 12
\]

Next, divide both sides by 4:

\[
x > 3
\]

2. **Inequality 2**: \( x + 6 > -2 \)

Subtract 6 from both sides:

\[
x > -8
\]

Now we combine the two solution sets:

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

Since \( x > 3 \) is a stronger condition than \( x > -8 \), the solution set is determined by \( x > 3 \).

Thus, the solution set is:

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

So, the response is:

\(\{ x \mid x > 3 \}\)