Question

Question

Find the solution set of 4x−3>9
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}
left brace x vertical bar x greater than 3 right brace
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Answer 1

To solve the compound inequalities $4x-3>9$ and $x+6>-2$, we will solve each inequality separately.

1. Solving $4x-3>9$: $$4x-3>9$$ Add 3 to both sides: $$4x>12$$ Divide by 4: $$x>3$$

2. Solving $x+6>-2$: $$x+6>-2$$ Subtract 6 from both sides: $$x>-8$$

Now, we have two inequalities:

• $x>3$
• $x>-8$

The solution set is the intersection of $x>3$ and $x>-8$. Since $x>3$ is more restrictive than $x>-8$, the solution set is simply:

$$x,|,x>3$$

Thus, the correct response is:

$x,|,x>3$ (which corresponds to your last option).