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Find the solution set of 4x−3>9 and x+6>−2 .(1 point)

Responses

{3,−8}
left brace 3 comma negative 8 right brace

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

The solution set is null.
The solution set is null.

{x|x>−8}

1 answer

To find the solution set for the inequalities \(4x - 3 > 9\) and \(x + 6 > -2\), let's solve each inequality individually.

  1. Solve \(4x - 3 > 9\): \[ 4x - 3 > 9 \] Add 3 to both sides: \[ 4x > 12 \] Divide by 4: \[ x > 3 \]

  2. Solve \(x + 6 > -2\): \[ x + 6 > -2 \] Subtract 6 from both sides: \[ x > -8 \]

Now, we combine the solutions:

  • The first inequality gives us \(x > 3\).
  • The second inequality gives us \(x > -8\).

Since \(x > 3\) is the stricter condition, the solution set for the combined inequalities is: \[ {x \mid x > 3} \]

So, the correct response is: \({x \mid x > 3}\) (left brace x vertical bar x greater than 3 right brace).