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

Question

?(1 point)
Responses

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

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

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

Answer 1

To determine which equation has the solution set \( x = {-95, 3} \), we can substitute the values into each equation to see if they produce a true statement (i.e., equal zero).

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

• For \( x = 3 \): \((3 - 3)(9(3) + 5) = 0 \cdot 32 = 0\) → true
• For \( x = -95 \): \((-95 - 3)(9(-95) + 5) = -98(-855) ≠ 0\) → false

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

• For \( x = 3 \): \(-3(3)(5(3) + 9) = -3(3)(24) = -216 ≠ 0\) → false
• For \( x = -95 \): \(-3(-95)(5(-95) + 9) = 0\) (first factor is \( 0 \)) → true

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

• For \( x = 3 \): \((3 - 3)(5(3) + 9) = 0 \cdot 24 = 0\) → true
• For \( x = -95 \): \((-95 - 3)(5(-95) + 9) = -98(-466) ≠ 0\) → false

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

• For \( x = 3 \): \((3 + 3)(9(3) - 5) = 6(22) = 132 ≠ 0\) → false
• For \( x = -95 \): \((-95 + 3)(9(-95) - 5) = -92(-860) ≠ 0\) → false

Conclusion

The only option that has \( 3 \) as a solution is Options 1 and 3, but neither has \( -95 \) as a solution.

Upon reviewing all, we find that none of these equations satisfy both values \( -95 \) and \( 3 \) as solutions.

However, let's confirm:

Review Option 2:

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

• The solutions would be \( x = 0 \) or \( 5x + 9 = 0 \) → \( x = -\frac{9}{5} = -1.8\) (neither of these is among \( -95 \) or \( 3\))

None of these correctly yield both \( -95 \) and \( 3 \).

Thus, there isn't a correct option among the given choices matching the solution set \( x = {-95, 3} \).