find the solution set of 4x−3>9and x+6>−2.(1 point)ResponsesThe 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{x|x>3}

Answer 1

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

1. Solve the first inequality: \[ 4x - 3 > 9 \] Add 3 to both sides: \[ 4x > 12 \] Now, divide both sides by 4: \[ x > 3 \]

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

3. Finding the intersection of the solution sets:

   • The solution set for the first inequality is \(x > 3\).
   • The solution set for the second inequality is \(x > -8\).

Now, we take the intersection of these two sets. Since \(x > 3\) is more restrictive than \(x > -8\), the solution to the combined inequalities is: \[ x > 3 \]

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

So, the correct response is: \[ { x \mid x > 3 } \]