Find the solution set of 4x−3>9

Question

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}
left brace x vertical bar x greater than negative 8 right brace

Answer 1

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

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

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

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

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

Now we have the two inequalities:

• \(x > 3\)
• \(x > -8\)

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

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

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