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 The solution set is null. The solution set is null. {x|x>−8}

Answer 1

To find the solution set, we need to solve each inequality separately.

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

   \[ 4x - 3 > 9 \] Add 3 to both sides: \[ 4x > 12 \] Divide both sides by 4: \[ x > 3 \]

2. Solve \(x + 6 > -2\):

   \[ x + 6 > -2 \] Subtract 6 from both sides: \[ x > -8 \]

Now we combine the solutions:

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

The more restrictive condition is \(x > 3\), since any value greater than 3 will also be greater than -8.

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

Therefore, the correct response is: \({x | x > 3}\).