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Simplifying -5a + 2b + -7c + 6c + -3b + 3a = 0 Reorder the terms: -5a + 3a + 2b + -3b + -7c + 6c = 0 Combine like terms: -5a + 3a = -2a -2a + 2b + -3b + -7c + 6c = 0 Combine like terms: 2b + -3b = -1b -2a + -1b + -7c + 6c = 0 Combine like terms: -7c + 6c = -1c -2a + -1b + -1c = 0 Solving -2a + -1b + -1c = 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. -2a + -1b + b + -1c = 0 + b Combine like terms: -1b + b = 0 -2a + 0 + -1c = 0 + b -2a + -1c = 0 + b Remove the zero: -2a + -1c = b Add 'c' to each side of the equation. -2a + -1c + c = b + c Combine like terms: -1c + c = 0 -2a + 0 = b + c -2a = b + c Divide each side by '-2'. a = -0.5b + -0.5c Simplifying a = -0.5b + -0.5c
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