To determine if \( x = 23 \) is a solution to the equation \( 9x^2 + 3x - 5 = 6 \), we can substitute \( x = 23 \) into the left-hand side of the equation and check if it equals 6.
First, substitute \( x = 23 \):
\[ 9(23^2) + 3(23) - 5 \]
Calculating \( 23^2 \):
\[ 23^2 = 529 \]
Now, substitute this value back into the equation:
\[ 9(529) + 3(23) - 5 = 4761 + 69 - 5 = 4825 \]
Now, we compare:
\[ 4825 \neq 6 \]
Since substituting \( x = 23 \) into the left hand side of the equation does not yield 6, we can conclude that \( x = 23 \) is not a solution.
Among the options, the correct reasoning would be:
No, x=23 is not a solution because substituting it back into the equation results in \( 4825 \neq 6 \), which is a false statement.
However, since this specific option is not listed in your responses, based on the available responses, the closest correct reasoning would be:
No, x=23 is not a solution because substituting it back into the equation results in \( 1 = 6 \), which is a false statement.
(This option is incorrect as '1' does not equal '6', but it's the only choice indicating that \( x=23 \) is not a solution.)
1 answer