To solve the factored quadratic equation \((13x + 3)(9x - 14) = 0\), we can set each factor to zero and solve for \(x\):
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First factor:
\(13x + 3 = 0\)
Subtract 3 from both sides:
\(13x = -3\)
Now, divide by 13:
\(x = -\frac{3}{13}\) -
Second factor:
\(9x - 14 = 0\)
Add 14 to both sides:
\(9x = 14\)
Now, divide by 9:
\(x = \frac{14}{9}\)
Now, we can compile the solutions together: The solution set is \(x = \left{-\frac{3}{13}, \frac{14}{9}\right}\).
Thus, the correct solution from the options provided is: The solution set is \(x = \left{-\frac{3}{13}, \frac{14}{9}\right}\).
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