Question

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

{x|x>−8}
start set x such that x is greater than negative 8 end set

{x|x>3}
start set x such that x is greater than 3 end set

{3,−8}
start set 3 comma negative 8 end set

The solution set is null.

Answer 1

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

1. Solve \(4x - 3 > 9\):
\[
4x - 3 > 9
\]
Add 3 to both sides:
\[
4x > 12
\]
Divide by 4:
\[
x > 3
\]

2. Solve \(x + 6 > -2\):
\[
x + 6 > -2
\]
Subtract 6 from both sides:
\[
x > -8
\]

Now we combine the two inequalities. The solution for \(x\) must satisfy both conditions:
- \(x > 3\)
- \(x > -8\)

Since \(x > 3\) is the more restrictive condition (any number greater than 3 is also greater than -8), the overall solution set is:
\[
\{x | x > 3\}
\]

So, the correct response is:
\(\{x | x > 3\}\) (start set x such that x is greater than 3 end set).