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Simplifying 7(3f + -2g) + 13(g + -1f) = 0 (3f * 7 + -2g * 7) + 13(g + -1f) = 0 (21f + -14g) + 13(g + -1f) = 0 Reorder the terms: 21f + -14g + 13(-1f + g) = 0 21f + -14g + (-1f * 13 + g * 13) = 0 21f + -14g + (-13f + 13g) = 0 Reorder the terms: 21f + -13f + -14g + 13g = 0 Combine like terms: 21f + -13f = 8f 8f + -14g + 13g = 0 Combine like terms: -14g + 13g = -1g 8f + -1g = 0 Solving 8f + -1g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add 'g' to each side of the equation. 8f + -1g + g = 0 + g Combine like terms: -1g + g = 0 8f + 0 = 0 + g 8f = 0 + g Remove the zero: 8f = g Divide each side by '8'. f = 0.125g Simplifying f = 0.125g
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