Which of the following equations has the solution set x={−95,3}

Question

?(1 point)
Responses

(x−3)(5x+9)=0
left parenthesis x minus 3 right parenthesis left parenthesis 5 x plus 9 right parenthesis equals 0

−3x(5x+9)=0
negative 3 x left parenthesis 5 x plus 9 right parenthesis equals 0

(x+3)(9x−5)=0
left parenthesis x plus 3 right parenthesis left parenthesis 9 x minus 5 right parenthesis equals 0

(x−3)(9x+5)=0

Answer 1

To determine which equation has the solution set \( x = {-95, 3} \), we can set each equation equal to zero and solve for \( x \).

1. Equation: \((x - 3)(5x + 9) = 0\)

   • Solutions:
     • \(x - 3 = 0 \rightarrow x = 3\)
     • \(5x + 9 = 0 \rightarrow 5x = -9 \rightarrow x = -\frac{9}{5}\)
   • Solution set: {3, -\frac{9}{5}}

2. Equation: \(-3x(5x + 9) = 0\)

   • Solutions:
     • \(-3x = 0 \rightarrow x = 0\)
     • \(5x + 9 = 0 \rightarrow 5x = -9 \rightarrow x = -\frac{9}{5}\)
   • Solution set: {0, -\frac{9}{5}}

3. Equation: \((x + 3)(9x - 5) = 0\)

   • Solutions:
     • \(x + 3 = 0 \rightarrow x = -3\)
     • \(9x - 5 = 0 \rightarrow 9x = 5 \rightarrow x = \frac{5}{9}\)
   • Solution set: {-3, \frac{5}{9}}

4. Equation: \((x - 3)(9x + 5) = 0\)

   • Solutions:
     • \(x - 3 = 0 \rightarrow x = 3\)
     • \(9x + 5 = 0 \rightarrow 9x = -5 \rightarrow x = -\frac{5}{9}\)
   • Solution set: {3, -\frac{5}{9}}

None of the provided equations gives a solution set of \({-95, 3}\).

If \( x = -95 \) is to be included in the solution set, let's analyze what that would require:

• Something like \((x + 95)(x - 3) = 0\) would give \(x = -95\) and \(x = 3\). But none of the available options produce this equation.

Thus, it appears there is no solution set among the options that equals \({-95, 3}\).