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Simplifying (4a + 3b + -1c) + -1(a + 5b + -3) = 0 Remove parenthesis around (4a + 3b + -1c) 4a + 3b + -1c + -1(a + 5b + -3) = 0 Reorder the terms: 4a + 3b + -1c + -1(-3 + a + 5b) = 0 4a + 3b + -1c + (-3 * -1 + a * -1 + 5b * -1) = 0 4a + 3b + -1c + (3 + -1a + -5b) = 0 Reorder the terms: 3 + 4a + -1a + 3b + -5b + -1c = 0 Combine like terms: 4a + -1a = 3a 3 + 3a + 3b + -5b + -1c = 0 Combine like terms: 3b + -5b = -2b 3 + 3a + -2b + -1c = 0 Solving 3 + 3a + -2b + -1c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 3a + -2b + -3 + -1c = 0 + -3 Reorder the terms: 3 + -3 + 3a + -2b + -1c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3a + -2b + -1c = 0 + -3 3a + -2b + -1c = 0 + -3 Combine like terms: 0 + -3 = -3 3a + -2b + -1c = -3 Add '2b' to each side of the equation. 3a + -2b + 2b + -1c = -3 + 2b Combine like terms: -2b + 2b = 0 3a + 0 + -1c = -3 + 2b 3a + -1c = -3 + 2b Add 'c' to each side of the equation. 3a + -1c + c = -3 + 2b + c Combine like terms: -1c + c = 0 3a + 0 = -3 + 2b + c 3a = -3 + 2b + c Divide each side by '3'. a = -1 + 0.6666666667b + 0.3333333333c Simplifying a = -1 + 0.6666666667b + 0.3333333333c
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