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

Question

Responses

{x|x>−8}
left brace x vertical bar x greater than negative 8 right brace
{3,−8}
left brace 3 comma negative 8 right brace
{x|x>3}
left brace x vertical bar x greater than 3 right brace
The solution set is null.

Answer 1

To find the solution set of 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 by 4: \[ x > 3 \]

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

Now we need to combine the two inequalities. The solution must satisfy both \(x > 3\) and \(x > -8\).

Since \(x > 3\) is a more restrictive condition than \(x > -8\), the combined solution set is given by \(x > 3\).

Thus, the solution set is \( { x \mid x > 3 } \).

The correct response is: {x | x > 3}