To solve the equation \( \frac{37.4775}{4.5k} + 3 = 2.63 \) for the variable \( k \), we first isolate the term involving \( k \).
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Start with the original equation: \[ \frac{37.4775}{4.5k} + 3 = 2.63 \]
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Subtract 3 from both sides to isolate the fraction: \[ \frac{37.4775}{4.5k} = 2.63 - 3 \]
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Simplifying the right side: \[ \frac{37.4775}{4.5k} = -0.37 \]
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Now, multiply both sides by \( 4.5k \) to eliminate the fraction: \[ 37.4775 = -0.37 \cdot 4.5k \]
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Calculate \( -0.37 \cdot 4.5 \): \[ -0.37 \cdot 4.5 = -1.665 \] So, the equation becomes: \[ 37.4775 = -1.665k \]
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Now, divide both sides by -1.665 to solve for \( k \): \[ k = \frac{37.4775}{-1.665} \]
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Compute the right side: \[ k \approx -22.486 \]
Therefore, the solution is: \[ k \approx -22.486 \]
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