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

Answer 1

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

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 results: We have two inequalities: \[ x > 3 \] and \[ x > -8 \]

   The more restrictive condition is \(x > 3\).

Thus, the solution set is: \[ \boxed{(3, \infty)} \]