To solve the equation \( 14(8 - 16g) + 8 = g \), we will use the properties of equality step by step.
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Distribute the 14: \[ 14(8) - 14(16g) + 8 = g \] Calculating \( 14(8) \) gives: \[ 112 - 224g + 8 = g \]
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Combine like terms: \[ 112 + 8 - 224g = g \] This simplifies to: \[ 120 - 224g = g \]
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Isolate the term involving \( g \): We can add \( 224g \) to both sides: \[ 120 = g + 224g \] This simplifies to: \[ 120 = 225g \]
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Solve for \( g \): Divide both sides by 225 to isolate \( g \): \[ g = \frac{120}{225} \]
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Simplify the fraction: To simplify \(\frac{120}{225}\), we can divide the numerator and denominator by their greatest common divisor, which is 15: \[ g = \frac{120 \div 15}{225 \div 15} = \frac{8}{15} \]
Thus, the solution to the equation is: \[ \boxed{\frac{8}{15}} \]
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