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Simplifying -3a + b + 3c + 7a + 11b + 15c = 0 Reorder the terms: -3a + 7a + b + 11b + 3c + 15c = 0 Combine like terms: -3a + 7a = 4a 4a + b + 11b + 3c + 15c = 0 Combine like terms: b + 11b = 12b 4a + 12b + 3c + 15c = 0 Combine like terms: 3c + 15c = 18c 4a + 12b + 18c = 0 Solving 4a + 12b + 18c = 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. 4a + 12b + -12b + 18c = 0 + -12b Combine like terms: 12b + -12b = 0 4a + 0 + 18c = 0 + -12b 4a + 18c = 0 + -12b Remove the zero: 4a + 18c = -12b Add '-18c' to each side of the equation. 4a + 18c + -18c = -12b + -18c Combine like terms: 18c + -18c = 0 4a + 0 = -12b + -18c 4a = -12b + -18c Divide each side by '4'. a = -3b + -4.5c Simplifying a = -3b + -4.5c
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