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).