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

Answer 1

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

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:

\[ x > -8 \]

3. Combine the solutions:

The solution sets we have are:

• From the first inequality: \(x > 3\)
• From the second inequality: \(x > -8\)

The intersection of these two inequalities is the more restrictive one:

Thus, the solution set for the combined inequalities is:

\[ x > 3 \]

This can be expressed in set notation as:

\[ {x \mid x > 3} \]

Therefore, the correct response is:

\({x \mid x > 3}\) (although this specific option isn't listed in your responses; you may want to present this derived answer).