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Simplifying (-5a + 3b + -1c) + -1(-9b + 3c + -7d) = 0 Remove parenthesis around (-5a + 3b + -1c) -5a + 3b + -1c + -1(-9b + 3c + -7d) = 0 -5a + 3b + -1c + (-9b * -1 + 3c * -1 + -7d * -1) = 0 -5a + 3b + -1c + (9b + -3c + 7d) = 0 Reorder the terms: -5a + 3b + 9b + -1c + -3c + 7d = 0 Combine like terms: 3b + 9b = 12b -5a + 12b + -1c + -3c + 7d = 0 Combine like terms: -1c + -3c = -4c -5a + 12b + -4c + 7d = 0 Solving -5a + 12b + -4c + 7d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12b' to each side of the equation. -5a + 12b + -4c + -12b + 7d = 0 + -12b Reorder the terms: -5a + 12b + -12b + -4c + 7d = 0 + -12b Combine like terms: 12b + -12b = 0 -5a + 0 + -4c + 7d = 0 + -12b -5a + -4c + 7d = 0 + -12b Remove the zero: -5a + -4c + 7d = -12b Add '4c' to each side of the equation. -5a + -4c + 4c + 7d = -12b + 4c Combine like terms: -4c + 4c = 0 -5a + 0 + 7d = -12b + 4c -5a + 7d = -12b + 4c Add '-7d' to each side of the equation. -5a + 7d + -7d = -12b + 4c + -7d Combine like terms: 7d + -7d = 0 -5a + 0 = -12b + 4c + -7d -5a = -12b + 4c + -7d Divide each side by '-5'. a = 2.4b + -0.8c + 1.4d Simplifying a = 2.4b + -0.8c + 1.4d
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