To determine whether the point (12, 31) is a solution to the inequality \( y > 4x - 17 \), we need to substitute \( x = 12 \) and \( y = 31 \) into the inequality and see if it holds true.
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Substitute \( x = 12 \) into the equation \( 4x - 17 \): \[ 4(12) - 17 = 48 - 17 = 31 \]
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Now, we need to check if \( y > 4x - 17 \): \[ 31 > 31 \]
This inequality \( 31 > 31 \) is not true because 31 is equal to 31, not greater than. Therefore, the point (12, 31) does not satisfy the inequality \( y > 4x - 17 \).
In conclusion, (12, 31) is not a solution to the inequality because it does not satisfy the condition of being greater than 31.
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