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Simplifying 3a + 2b + -1c + -1d = 0 Solving 3a + 2b + -1c + -1d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 3a + 2b + -1c + -2b + -1d = 0 + -2b Reorder the terms: 3a + 2b + -2b + -1c + -1d = 0 + -2b Combine like terms: 2b + -2b = 0 3a + 0 + -1c + -1d = 0 + -2b 3a + -1c + -1d = 0 + -2b Remove the zero: 3a + -1c + -1d = -2b Add 'c' to each side of the equation. 3a + -1c + c + -1d = -2b + c Combine like terms: -1c + c = 0 3a + 0 + -1d = -2b + c 3a + -1d = -2b + c Add 'd' to each side of the equation. 3a + -1d + d = -2b + c + d Combine like terms: -1d + d = 0 3a + 0 = -2b + c + d 3a = -2b + c + d Divide each side by '3'. a = -0.6666666667b + 0.3333333333c + 0.3333333333d Simplifying a = -0.6666666667b + 0.3333333333c + 0.3333333333d
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