To determine which equation has the solution set \( x = {-95, 3} \), we need to analyze each of the given equations and find their corresponding roots (solutions).
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First equation: \(-3x(5x + 9) = 0\)
Set each factor to zero:
\(-3x = 0 \Rightarrow x = 0\)
\(5x + 9 = 0 \Rightarrow 5x = -9 \Rightarrow x = -\frac{9}{5}\)
Solutions: \(0, -\frac{9}{5}\) -
Second equation: \((x - 3)(9x + 5) = 0\)
Set each factor to zero:
\(x - 3 = 0 \Rightarrow x = 3\)
\(9x + 5 = 0 \Rightarrow 9x = -5 \Rightarrow x = -\frac{5}{9}\)
Solutions: \(3, -\frac{5}{9}\) -
Third equation: \((x - 3)(5x + 9) = 0\)
Set each factor to zero:
\(x - 3 = 0 \Rightarrow x = 3\)
\(5x + 9 = 0 \Rightarrow 5x = -9 \Rightarrow x = -\frac{9}{5}\)
Solutions: \(3, -\frac{9}{5}\) -
Fourth equation: \((x + 3)(9x - 5) = 0\)
Set each factor to zero:
\(x + 3 = 0 \Rightarrow x = -3\)
\(9x - 5 = 0 \Rightarrow 9x = 5 \Rightarrow x = \frac{5}{9}\)
Solutions: \(-3, \frac{5}{9}\)
None of the listed equations yielded the solutions \(-95\) and \(3\). To find an equation that yields these solutions, we could construct it from the roots directly.
An equation that would yield the solutions \(x = -95\) and \(x = 3\) would be: \[ (x - 3)(x + 95) = 0 \] This is not one of the options provided.
Among the given options, none match the solution set \( x = {-95, 3} \).