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Simplifying (-5a + 7b + -1c) + -1(-9b + 5c + -2d) = 0 Remove parenthesis around (-5a + 7b + -1c) -5a + 7b + -1c + -1(-9b + 5c + -2d) = 0 -5a + 7b + -1c + (-9b * -1 + 5c * -1 + -2d * -1) = 0 -5a + 7b + -1c + (9b + -5c + 2d) = 0 Reorder the terms: -5a + 7b + 9b + -1c + -5c + 2d = 0 Combine like terms: 7b + 9b = 16b -5a + 16b + -1c + -5c + 2d = 0 Combine like terms: -1c + -5c = -6c -5a + 16b + -6c + 2d = 0 Solving -5a + 16b + -6c + 2d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16b' to each side of the equation. -5a + 16b + -6c + -16b + 2d = 0 + -16b Reorder the terms: -5a + 16b + -16b + -6c + 2d = 0 + -16b Combine like terms: 16b + -16b = 0 -5a + 0 + -6c + 2d = 0 + -16b -5a + -6c + 2d = 0 + -16b Remove the zero: -5a + -6c + 2d = -16b Add '6c' to each side of the equation. -5a + -6c + 6c + 2d = -16b + 6c Combine like terms: -6c + 6c = 0 -5a + 0 + 2d = -16b + 6c -5a + 2d = -16b + 6c Add '-2d' to each side of the equation. -5a + 2d + -2d = -16b + 6c + -2d Combine like terms: 2d + -2d = 0 -5a + 0 = -16b + 6c + -2d -5a = -16b + 6c + -2d Divide each side by '-5'. a = 3.2b + -1.2c + 0.4d Simplifying a = 3.2b + -1.2c + 0.4d
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