Find the solution set of 4x−3>9 and x+6>−2 .(1 point) Responses {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. {x|x>3} left brace x vertical bar x greater than 3 right brace {3,−8}

Answer 1

To solve the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we will analyze 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 have two inequalities:

• \(x > 3\)
• \(x > -8\)

The solution set for both inequalities is the overlap of both solutions. The more restrictive condition is \(x > 3\), since any number greater than 3 will also be greater than -8.

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

The correct response is: \({x ,|, x > 3}\) or, in your format, \(\text{left brace } x \text{ vertical bar } x > 3 \text{ right brace}\).