Ask a New Question
Menu

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

𝑥
=
{
−
9
5
,
3
}
?(1 point)
Responses

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

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

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

(x−3)(9x+5)=0

3 answers

To determine which of the provided equations has the solution set \( x = {-95, 3} \), we can analyze each equation one by one:

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

    • Set \( x + 3 = 0 \) gives \( x = -3 \).
    • Set \( 9x - 5 = 0 \) gives \( 9x = 5 \Rightarrow x = \frac{5}{9} \).
    • Solutions: \( x = -3, \frac{5}{9} \) (Not our set).

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

    • Set \( x - 3 = 0 \) gives \( x = 3 \).
    • Set \( 5x + 9 = 0 \) gives \( 5x = -9 \Rightarrow x = -\frac{9}{5} \).
    • Solutions: \( x = 3, -\frac{9}{5} \) (Not our set).

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

    • Set \( -3x = 0 \) gives \( x = 0 \).
    • Set \( 5x + 9 = 0 \) gives \( 5x = -9 \Rightarrow x = -\frac{9}{5} \).
    • Solutions: \( x = 0, -\frac{9}{5} \) (Not our set).

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

    • Set \( x - 3 = 0 \) gives \( x = 3 \).
    • Set \( 9x + 5 = 0 \) gives \( 9x = -5 \Rightarrow x = -\frac{5}{9} \).
    • Solutions: \( x = 3, -\frac{5}{9} \) (Not our set).

Since none of the provided options yield the solutions \( -95 \) or \( 3 \), there must be an error in provided equations. For the correct solution set, the equation should give \( x = -95 \) and \( x = 3 \).

The factorization that provides these roots should look like: \[ (x - 3)(x + 95) = 0 \] Hence, if this option was present, it would be the correct one.

Final Answer: None of the provided equations have the solution set \( x = {-95, 3} \).

you have to choose one

Based on your request and considering that we need to choose one of the provided options, the closest equation that correctly provides one of the desired roots, \(3\), would be:

(x - 3)(5x + 9) = 0

This equation yields a solution of \(x = 3\), but does not yield \(-95\). However, since it's the only option that includes \(3\), I would select this one:

Answer: (x - 3)(5x + 9) = 0