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

Question

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

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

(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

Answer 1

To determine which equation has the solution set \( x = {-95, 3} \), we need to look for a factored form that yields these solutions.

1. The first option is \( (x-3)(9x+5)=0 \).

• The solutions are \( x - 3 = 0 \) or \( 9x + 5 = 0 \).
• From \( x - 3 = 0 \), we get \( x = 3 \).
• From \( 9x + 5 = 0 \), we have \( 9x = -5 \) or \( x = -\frac{5}{9} \).
• The solution set is \( {3, -\frac{5}{9}} \).

2. The second option is \( (x+3)(9x-5)=0 \).

• The solutions are \( x + 3 = 0 \) or \( 9x - 5 = 0 \).
• From \( x + 3 = 0 \), we get \( x = -3 \).
• From \( 9x - 5 = 0 \), we have \( 9x = 5 \) or \( x = \frac{5}{9} \).
• The solution set is \( {-3, \frac{5}{9}} \).

3. The third option is \( (x-3)(5x+9)=0 \).

• The solutions are \( x - 3 = 0 \) or \( 5x + 9 = 0 \).
• From \( x - 3 = 0 \), we get \( x = 3 \).
• From \( 5x + 9 = 0 \), we have \( 5x = -9 \) or \( x = -\frac{9}{5} \).
• The solution set is \( {3, -\frac{9}{5}} \).

4. The fourth option is \( -3x(5x+9)=0 \).

• The solutions are \( -3x = 0 \) or \( 5x + 9 = 0 \).
• From \( -3x = 0 \), we get \( x = 0 \).
• From \( 5x + 9 = 0 \), we have \( 5x = -9 \) or \( x = -\frac{9}{5} \).
• The solution set is \( {0, -\frac{9}{5}} \).

None of the options seem to yield the desired solution set of \( {-95, 3} \).

However, let’s analyze the context again:

The desired solutions can also be derived from the equation in the factored form as follows:

\[ (x - 3)(x + 95) = 0 \]

This would give us the solutions \( x = 3 \) and \( x = -95 \).

To summarize, it seems none of the options given provide the correct solution set explicitly as they are based on different constant multipliers.

Thus, if we were analyzing the potential for a typo in the options or miscommunication in interpretation, it’s worth noting that the correct equation should be \( (x - 3)(x + 95) = 0 \) to yield the desired solution set \( {-95, 3} \).

If forced to select from the options, the first gives a variant close but incorrect due to the wrong coefficients in subsequent solutions derived.

Bottom Line: None of the provided options yield the required solution set. The correct polynomial should be factored explicitly as noted above.