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5. Find the solution set of 4x−3>9

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}

1 answer

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

  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 combine the two solutions:

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

Since \(x > 3\) is more restrictive than \(x > -8\), the combined solution is: \[ x > 3 \]

Final Solution Set: The solution set is \({x | x > 3}\).

Therefore, the correct response is: \[ {x | x > 3} \]