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Simplifying 7(3f + -2g) + 14(f + -1g) = 0 (3f * 7 + -2g * 7) + 14(f + -1g) = 0 (21f + -14g) + 14(f + -1g) = 0 21f + -14g + (f * 14 + -1g * 14) = 0 21f + -14g + (14f + -14g) = 0 Reorder the terms: 21f + 14f + -14g + -14g = 0 Combine like terms: 21f + 14f = 35f 35f + -14g + -14g = 0 Combine like terms: -14g + -14g = -28g 35f + -28g = 0 Solving 35f + -28g = 0 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '28g' to each side of the equation. 35f + -28g + 28g = 0 + 28g Combine like terms: -28g + 28g = 0 35f + 0 = 0 + 28g 35f = 0 + 28g Remove the zero: 35f = 28g Divide each side by '35'. f = 0.8g Simplifying f = 0.8g
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