To determine if \( x = \frac{2}{3} \) is a solution to the equation \( 9x^2 + 3x - 5 = 6 \), we need to substitute \( x = \frac{2}{3} \) into the equation and see if both sides are equal.
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Start with the left side: \( 9\left(\frac{2}{3}\right)^2 + 3\left(\frac{2}{3}\right) - 5 \).
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Calculate \( 9\left(\frac{2}{3}\right)^2 \): \[ 9\left(\frac{4}{9}\right) = 4. \]
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Calculate \( 3\left(\frac{2}{3}\right) \): \[ 3 \cdot \frac{2}{3} = 2. \]
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Now combine these results: \[ 4 + 2 - 5 = 1. \]
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The equation becomes: \[ 1 = 6, \] which is false.
Since substituting \( x = \frac{2}{3} \) into the equation does not yield a true statement (1 does not equal 6), we can conclude that \( x = \frac{2}{3} \) is not a solution.
The best explanation from your options would be:
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.
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