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Simplifying 8f + 7g + -2f + -3g + 4f + 2g + -9f + -5g + 1g = 0 Reorder the terms: 8f + -2f + 4f + -9f + 7g + -3g + 2g + -5g + 1g = 0 Combine like terms: 8f + -2f = 6f 6f + 4f + -9f + 7g + -3g + 2g + -5g + 1g = 0 Combine like terms: 6f + 4f = 10f 10f + -9f + 7g + -3g + 2g + -5g + 1g = 0 Combine like terms: 10f + -9f = 1f 1f + 7g + -3g + 2g + -5g + 1g = 0 Combine like terms: 7g + -3g = 4g 1f + 4g + 2g + -5g + 1g = 0 Combine like terms: 4g + 2g = 6g 1f + 6g + -5g + 1g = 0 Combine like terms: 6g + -5g = 1g 1f + 1g + 1g = 0 Combine like terms: 1g + 1g = 2g 1f + 2g = 0 Solving 1f + 2g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-2g' to each side of the equation. 1f + 2g + -2g = 0 + -2g Combine like terms: 2g + -2g = 0 1f + 0 = 0 + -2g 1f = 0 + -2g Remove the zero: 1f = -2g Divide each side by '1'. f = -2g Simplifying f = -2g
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