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

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

The solution set is null.
The solution set is null.

{3,−8}

Answer 1

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

1. Solving the first inequality: \[ 4x - 3 > 9 \] Add 3 to both sides: \[ 4x > 12 \] Divide both sides by 4: \[ x > 3 \]

2. Solving the second inequality: \[ x + 6 > -2 \] Subtract 6 from both sides: \[ x > -8 \]

Now we have two inequalities:

• \(x > 3\)
• \(x > -8\)

The solution set that satisfies both of these inequalities is the more restrictive one, which is \(x > 3\).

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

The correct response is: \({x \mid x > 3}\) (left brace x vertical bar x greater than 3 right brace).