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Simplifying 4F + 5g + 6f + -7g + f = 0 Reorder the terms: 4F + 6f + f + 5g + -7g = 0 Combine like terms: 6f + f = 7f 4F + 7f + 5g + -7g = 0 Combine like terms: 5g + -7g = -2g 4F + 7f + -2g = 0 Solving 4F + 7f + -2g = 0 Solving for variable 'F'. Move all terms containing F to the left, all other terms to the right. Add '-7f' to each side of the equation. 4F + 7f + -7f + -2g = 0 + -7f Combine like terms: 7f + -7f = 0 4F + 0 + -2g = 0 + -7f 4F + -2g = 0 + -7f Remove the zero: 4F + -2g = -7f Add '2g' to each side of the equation. 4F + -2g + 2g = -7f + 2g Combine like terms: -2g + 2g = 0 4F + 0 = -7f + 2g 4F = -7f + 2g Divide each side by '4'. F = -1.75f + 0.5g Simplifying F = -1.75f + 0.5g
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