Find the solution set of 4x−3>9

Question

and x+6>−2
.(1 point)
Responses

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

{3,−8}

Answer 1

To solve the inequalities:

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

   First, add 3 to both sides:

   \[ 4x > 12 \]

   Next, divide both sides by 4:

   \[ x > 3 \]

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

   Subtract 6 from both sides:

   \[ x > -8 \]

Now we combine the two solution sets:

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

Since \( x > 3 \) is a stronger condition than \( x > -8 \), the solution set is determined by \( x > 3 \).

Thus, the solution set is:

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

So, the response is:

\({ x \mid x > 3 }\)