Find the solution set of 4x−3>9

Question

and x+6>−2
.(1 point)
Responses

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

{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

{x|x>3}

Answer 1

To solve the inequalities, we will consider each one separately.

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

   \[ 4x > 9 + 3 \] \[ 4x > 12 \] \[ x > 3 \]

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

   \[ x > -2 - 6 \] \[ x > -8 \]

Now we need to find the solution set that satisfies both inequalities:

• From the first inequality, we have \( x > 3 \).
• From the second inequality, we have \( x > -8 \).

The more restrictive condition is \( x > 3 \). Therefore, the solution set is:

\[ {x | x > 3} \]

Thus, the correct answer from the options provided is:

\({x | x > 3}\)