Find the solution set of 4x−3>9 and x+6>−2

Question

.(1 point)
Responses

A) {x|x>3}
left brace x vertical bar x greater than 3 right brace

B) {x|x>−8}
left brace x vertical bar x greater than negative 8 right brace

C) The solution set is null.

D) {3,−8}

Answer 1

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

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

   Add 3 to both sides:
   \(4x > 12\)

   Divide by 4:
   \(x > 3\)

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

   Subtract 6 from both sides:
   \(x > -8\)

Now we have the two inequalities:

• \(x > 3\)
• \(x > -8\)

The more restrictive condition is \(x > 3\) since any number greater than 3 is also greater than -8. Thus, the solution set is:

\[ {x | x > 3} \]

Therefore, the correct response is:

A) {x | x > 3}