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

Question

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

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

The solution set is null.
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 both sides by 4: \[ x > 3 \]

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

Now we have the two solutions:

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

The solution set is determined by the more restrictive condition, which is \(x > 3\).

Thus, the solution set can be expressed as: \[ {x | x > 3} \]

So, the correct response is: {x | x > 3}