Find the solution set of 4x−3>9

Question

and x+6>−2
.(2 points)
Responses

The solution set is null
The solution set is null

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

{3, −8}
{3, −8}

{x | x>−8}

Answer 1

To solve the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), we can solve each inequality separately and then find the intersection of the two solution sets.

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

\[ 4x - 3 > 9 \] Add 3 to both sides:

\[ 4x > 12 \] Now, divide both sides by 4:

\[ x > 3 \]

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

\[ x + 6 > -2 \] Subtract 6 from both sides:

\[ x > -8 \]

Now we have the two solution sets:

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

To find the combined solution set, we take the intersection of both conditions. The solution set is:

\[ x > 3 \]

Thus, the correct response is:

{x | x > 3}