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Simplifying (-2b + a + -5c) + -1(3c + 5a + -1b) = 0 Reorder the terms: (a + -2b + -5c) + -1(3c + 5a + -1b) = 0 Remove parenthesis around (a + -2b + -5c) a + -2b + -5c + -1(3c + 5a + -1b) = 0 Reorder the terms: a + -2b + -5c + -1(5a + -1b + 3c) = 0 a + -2b + -5c + (5a * -1 + -1b * -1 + 3c * -1) = 0 a + -2b + -5c + (-5a + 1b + -3c) = 0 Reorder the terms: a + -5a + -2b + 1b + -5c + -3c = 0 Combine like terms: a + -5a = -4a -4a + -2b + 1b + -5c + -3c = 0 Combine like terms: -2b + 1b = -1b -4a + -1b + -5c + -3c = 0 Combine like terms: -5c + -3c = -8c -4a + -1b + -8c = 0 Solving -4a + -1b + -8c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. -4a + -1b + b + -8c = 0 + b Combine like terms: -1b + b = 0 -4a + 0 + -8c = 0 + b -4a + -8c = 0 + b Remove the zero: -4a + -8c = b Add '8c' to each side of the equation. -4a + -8c + 8c = b + 8c Combine like terms: -8c + 8c = 0 -4a + 0 = b + 8c -4a = b + 8c Divide each side by '-4'. a = -0.25b + -2c Simplifying a = -0.25b + -2c
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