Question

Solve the factored quadratic equation (13x+3)(9x−14)=0
.(1 point)
Responses

The solution set is x={−313,914}
.
The solution set is x equals left brace negative Start Fraction 3 over 13 End Fraction comma Start Fraction 9 over 14 End Fraction right brace .

The solution set is x={−313,159}
.
The solution set is x equals left brace negative Start Fraction 3 over 13 End Fraction comma 1 Start Fraction 5 over 9 End Fraction right brace .

The solution set is x={−3,14}
.
The solution set is x equals left brace negative 3 comma 14 right brace .

The solution set is x={−133,914}
.

Answer 1

To solve the factored quadratic equation \((13x + 3)(9x - 14) = 0\), we can set each factor equal to zero:

1. **First factor:** \(13x + 3 = 0\)
\[
13x = -3 \quad \Rightarrow \quad x = -\frac{3}{13}
\]

2. **Second factor:** \(9x - 14 = 0\)
\[
9x = 14 \quad \Rightarrow \quad x = \frac{14}{9}
\]

Thus, the solution set is:
\[
x = \left\{-\frac{3}{13}, \frac{14}{9}\right\}
\]

Therefore, the correct response is:
**The solution set is \(x = \left\{-\frac{3}{13}, \frac{14}{9}\right\}\).**