Find the solution set of 4x − 3 > 9 and x + 6 > −2.

Question

(1 point)
Responses

{x|x > 3}
{x|x > 3}

{x|x > −8}
{x|x > −8}

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

{3, −8}

Answer 1

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

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

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

Now we combine the results:

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

The solution set that satisfies both inequalities is the intersection of the two solutions: Since \( x > 3 \) is more restrictive than \( x > -8 \), the solution set is: \[ { x \mid x > 3 } \]

So, the correct response is: {x | x > 3}.