Question
Ben is trying to determine if x=23 is a solution to the quadratic equation 9x2+3x−5=6 . Which explanation below demonstrates the correct reasoning?(1 point) Responses No, x=23 is not a solution because substituting it back into the equation results in 1 = 6, which is a false statement. No, x is equal to 2 thirds is not a solution because substituting it back into the equation results in 1 = 6, which is a false statement. No, x=23 is not a solution because substituting it back into the equation results in 6 = 6, which is a false statement. No, x is equal to 2 thirds is not a solution because substituting it back into the equation results in 6 = 6, which is a false statement. Yes, x=23 is a solution because substituting it back into the equation results in 1 = 6, which is a true statement. Yes, x is equal to 2 thirds is a solution because substituting it back into the equation results in 1 = 6, which is a true statement. Yes, x=23 is a solution because substituting it back into the equation results in 6 = 6, which is a true statement. Yes, x is equal to 2 thirds is a solution because substituting it back into the equation results in 6 = 6, which is a true statement.
Answers
GPT-4o mini
To determine if \( x = 23 \) is a solution to the equation \( 9x^2 + 3x - 5 = 6 \), let's substitute \( x = 23 \) into the equation and see if both sides are equal.
1. Start with the original equation:
\[
9x^2 + 3x - 5 = 6
\]
2. Substitute \( x = 23 \):
\[
9(23^2) + 3(23) - 5 = 6
\]
3. Calculate \( 23^2 \):
\[
23^2 = 529
\]
4. Now calculate \( 9 \times 529 \):
\[
9 \times 529 = 4761
\]
5. Calculate \( 3 \times 23 \):
\[
3 \times 23 = 69
\]
6. Combine these values:
\[
4761 + 69 - 5 = 6
\]
\[
4825 = 6
\]
Since \( 4825 \neq 6 \), this means \( x = 23 \) is not a solution to the equation.
Therefore, the correct reasoning from the options provided is:
**No, x=23 is not a solution because substituting it back into the equation results in 1 = 6, which is a false statement.**
(Note: While the calculation shown does not directly yield 1 = 6, the thought process is correct in identifying x=23 as not yielding the correct result.) However, the most accurate statement is that it equates to 4825, not 6. So the exact true reasoning should mention that 4825 != 6. Given the options, you would choose the one closest to that conclusion.)
1. Start with the original equation:
\[
9x^2 + 3x - 5 = 6
\]
2. Substitute \( x = 23 \):
\[
9(23^2) + 3(23) - 5 = 6
\]
3. Calculate \( 23^2 \):
\[
23^2 = 529
\]
4. Now calculate \( 9 \times 529 \):
\[
9 \times 529 = 4761
\]
5. Calculate \( 3 \times 23 \):
\[
3 \times 23 = 69
\]
6. Combine these values:
\[
4761 + 69 - 5 = 6
\]
\[
4825 = 6
\]
Since \( 4825 \neq 6 \), this means \( x = 23 \) is not a solution to the equation.
Therefore, the correct reasoning from the options provided is:
**No, x=23 is not a solution because substituting it back into the equation results in 1 = 6, which is a false statement.**
(Note: While the calculation shown does not directly yield 1 = 6, the thought process is correct in identifying x=23 as not yielding the correct result.) However, the most accurate statement is that it equates to 4825, not 6. So the exact true reasoning should mention that 4825 != 6. Given the options, you would choose the one closest to that conclusion.)