To determine if \( x = \frac{3}{19} \) is a solution of the equation \( 15x + 4x + 6 = 9 \), we will substitute \( x \) with \( \frac{3}{19} \) and check if the left side of the equation equals the right side.
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Combine the terms on the left-hand side: \[ 15x + 4x + 6 = (15 + 4)x + 6 = 19x + 6 \]
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Substitute \( x \) with \( \frac{3}{19} \): \[ 19 \left(\frac{3}{19}\right) + 6 = 3 + 6 = 9 \]
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Compare to the right-hand side of the equation: \[ 9 = 9 \]
Since the left side equals the right side when \( x = \frac{3}{19} \), we conclude that \( \frac{3}{19} \) is indeed a solution of the equation.