Solve the factored quadratic equations (19x−3)(9+x)=0 (1 point) Responses The solution set is {193, 9} The solution set is {193, 9} The solution set is {−9, 193} The solution set is {−9, 193} The solution set is {−9, 319} The solution set is {−9, 319} The solution set is {−9, 3}

Answer 1

To solve the factored quadratic equation \((19x−3)(9+x)=0\), we will set each factor equal to zero and solve for \(x\).

1. Set the first factor equal to zero: \[ 19x - 3 = 0 \] Adding \(3\) to both sides gives: \[ 19x = 3 \] Dividing both sides by \(19\) gives: \[ x = \frac{3}{19} \]

2. Set the second factor equal to zero: \[ 9 + x = 0 \] Subtracting \(9\) from both sides gives: \[ x = -9 \]

Now we have the two solutions: \[ x = \frac{3}{19} \quad \text{and} \quad x = -9 \]

Thus, the solution set is: \[ \left{-9, \frac{3}{19}\right} \]

Since \(\frac{3}{19} \approx 0.158\), the solutions can be presented as: \[ \text{Solution Set is } {-9, \frac{3}{19}} \]

Given the multiple choice answers you provided, none match this exact solution. If you are looking for an approximate decimal value or a specific context for the answer, please let me know!

Answer 2

Pick one

Answer 3

Given the multiple choice answers you provided, the closest fit based on the calculated solutions is:

The solution set is \({-9, 193}\), which appears similar to \({-9, \frac{3}{19}}\) but is not accurate. Since \(\frac{3}{19}\) is approximately \(0.158\), it does not match any of the available responses exactly.

However, due to your request to pick one, I will choose:

The solution set is \({-9, 193}\) but recognize that the correct solution is actually \({-9, \frac{3}{19}}\).