Find the solution set of 4x−3>9

Question

and x+6>−2
.(1 point)
Responses

{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.

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

Answer 1

To solve the compound inequalities given, we will solve each inequality separately.

1. For the first inequality: \[ 4x - 3 > 9 \] We add 3 to both sides: \[ 4x > 12 \] Now, divide both sides by 4: \[ x > 3 \]

2. For the second inequality: \[ x + 6 > -2 \] We subtract 6 from both sides: \[ x > -8 \]

Now, combining both inequalities, we are looking for values of \( x \) that satisfy both: \[ x > 3 \quad \text{and} \quad x > -8 \]

Since \( x > 3 \) is a stricter condition than \( x > -8 \), the solution to the compound inequalities is simply: \[ x > 3 \]

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

Therefore, the correct response is: \[ {x | x > 3} \] (left brace x vertical bar x greater than 3 right brace).