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 {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.

Answer 1

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

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

2. **Solving the second inequality:**
\[
x + 6 > -2
\]
Subtract 6 from both sides:
\[
x > -8
\]

Now, we need to find the values of \(x\) that satisfy both inequalities \(x > 3\) and \(x > -8\). The more restrictive condition here is \(x > 3\).

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

Therefore, the answer is:
\[
\{x \mid x > 3\}
\]