To determine if the values \( x = 4 \) and \( x = 6 \) are solutions to the quadratic equation represented as \( 22 - 10x + 24 = 0 \), we first need to simplify the equation.
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Combine like terms: \[ 22 + 24 - 10x = 0 \] \[ 46 - 10x = 0 \]
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Rearranging this gives: \[ 10x = 46 \] \[ x = \frac{46}{10} = 4.6 \]
Now, we will check both values:
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For \( x = 4 \): \[ 46 - 10(4) = 46 - 40 = 6 \quad (\text{not } 0) \]
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For \( x = 6 \): \[ 46 - 10(6) = 46 - 60 = -14 \quad (\text{not } 0) \]
Since neither \( x = 4 \) nor \( x = 6 \) satisfies the equation \( 22 - 10x + 24 = 0 \), we find:
The correct answer is: Neither \( x = 4 \) nor \( x = 6 \) is a solution.