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Simplifying 2a + -1(3b + 2c) + (a + -3c) + -1(5a + -1b + 2c) = 0 2a + (3b * -1 + 2c * -1) + (a + -3c) + -1(5a + -1b + 2c) = 0 2a + (-3b + -2c) + (a + -3c) + -1(5a + -1b + 2c) = 0 Remove parenthesis around (a + -3c) 2a + -3b + -2c + a + -3c + -1(5a + -1b + 2c) = 0 2a + -3b + -2c + a + -3c + (5a * -1 + -1b * -1 + 2c * -1) = 0 2a + -3b + -2c + a + -3c + (-5a + 1b + -2c) = 0 Reorder the terms: 2a + a + -5a + -3b + 1b + -2c + -3c + -2c = 0 Combine like terms: 2a + a = 3a 3a + -5a + -3b + 1b + -2c + -3c + -2c = 0 Combine like terms: 3a + -5a = -2a -2a + -3b + 1b + -2c + -3c + -2c = 0 Combine like terms: -3b + 1b = -2b -2a + -2b + -2c + -3c + -2c = 0 Combine like terms: -2c + -3c = -5c -2a + -2b + -5c + -2c = 0 Combine like terms: -5c + -2c = -7c -2a + -2b + -7c = 0 Solving -2a + -2b + -7c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. -2a + -2b + 2b + -7c = 0 + 2b Combine like terms: -2b + 2b = 0 -2a + 0 + -7c = 0 + 2b -2a + -7c = 0 + 2b Remove the zero: -2a + -7c = 2b Add '7c' to each side of the equation. -2a + -7c + 7c = 2b + 7c Combine like terms: -7c + 7c = 0 -2a + 0 = 2b + 7c -2a = 2b + 7c Divide each side by '-2'. a = -1b + -3.5c Simplifying a = -1b + -3.5c
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