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Simplifying (-6d + 11e + -1f) + -1(9e + -4d + 6f) = 0 Remove parenthesis around (-6d + 11e + -1f) -6d + 11e + -1f + -1(9e + -4d + 6f) = 0 Reorder the terms: -6d + 11e + -1f + -1(-4d + 9e + 6f) = 0 -6d + 11e + -1f + (-4d * -1 + 9e * -1 + 6f * -1) = 0 -6d + 11e + -1f + (4d + -9e + -6f) = 0 Reorder the terms: -6d + 4d + 11e + -9e + -1f + -6f = 0 Combine like terms: -6d + 4d = -2d -2d + 11e + -9e + -1f + -6f = 0 Combine like terms: 11e + -9e = 2e -2d + 2e + -1f + -6f = 0 Combine like terms: -1f + -6f = -7f -2d + 2e + -7f = 0 Solving -2d + 2e + -7f = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-2e' to each side of the equation. -2d + 2e + -2e + -7f = 0 + -2e Combine like terms: 2e + -2e = 0 -2d + 0 + -7f = 0 + -2e -2d + -7f = 0 + -2e Remove the zero: -2d + -7f = -2e Add '7f' to each side of the equation. -2d + -7f + 7f = -2e + 7f Combine like terms: -7f + 7f = 0 -2d + 0 = -2e + 7f -2d = -2e + 7f Divide each side by '-2'. d = e + -3.5f Simplifying d = e + -3.5f
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