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Simplifying (-9a + 2b + -1c) + -1(5b + 5c + -2d) = 0 Remove parenthesis around (-9a + 2b + -1c) -9a + 2b + -1c + -1(5b + 5c + -2d) = 0 -9a + 2b + -1c + (5b * -1 + 5c * -1 + -2d * -1) = 0 -9a + 2b + -1c + (-5b + -5c + 2d) = 0 Reorder the terms: -9a + 2b + -5b + -1c + -5c + 2d = 0 Combine like terms: 2b + -5b = -3b -9a + -3b + -1c + -5c + 2d = 0 Combine like terms: -1c + -5c = -6c -9a + -3b + -6c + 2d = 0 Solving -9a + -3b + -6c + 2d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. -9a + -3b + -6c + 3b + 2d = 0 + 3b Reorder the terms: -9a + -3b + 3b + -6c + 2d = 0 + 3b Combine like terms: -3b + 3b = 0 -9a + 0 + -6c + 2d = 0 + 3b -9a + -6c + 2d = 0 + 3b Remove the zero: -9a + -6c + 2d = 3b Add '6c' to each side of the equation. -9a + -6c + 6c + 2d = 3b + 6c Combine like terms: -6c + 6c = 0 -9a + 0 + 2d = 3b + 6c -9a + 2d = 3b + 6c Add '-2d' to each side of the equation. -9a + 2d + -2d = 3b + 6c + -2d Combine like terms: 2d + -2d = 0 -9a + 0 = 3b + 6c + -2d -9a = 3b + 6c + -2d Divide each side by '-9'. a = -0.3333333333b + -0.6666666667c + 0.2222222222d Simplifying a = -0.3333333333b + -0.6666666667c + 0.2222222222d
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