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Simplifying 5a + 3b + 2c = 3a + -3b + 3c Solving 5a + 3b + 2c = 3a + -3b + 3c Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3a' to each side of the equation. 5a + 3b + -3a + 2c = 3a + -3b + -3a + 3c Reorder the terms: 5a + -3a + 3b + 2c = 3a + -3b + -3a + 3c Combine like terms: 5a + -3a = 2a 2a + 3b + 2c = 3a + -3b + -3a + 3c Reorder the terms: 2a + 3b + 2c = 3a + -3a + -3b + 3c Combine like terms: 3a + -3a = 0 2a + 3b + 2c = 0 + -3b + 3c 2a + 3b + 2c = -3b + 3c Add '-3b' to each side of the equation. 2a + 3b + -3b + 2c = -3b + -3b + 3c Combine like terms: 3b + -3b = 0 2a + 0 + 2c = -3b + -3b + 3c 2a + 2c = -3b + -3b + 3c Combine like terms: -3b + -3b = -6b 2a + 2c = -6b + 3c Add '-2c' to each side of the equation. 2a + 2c + -2c = -6b + 3c + -2c Combine like terms: 2c + -2c = 0 2a + 0 = -6b + 3c + -2c 2a = -6b + 3c + -2c Combine like terms: 3c + -2c = 1c 2a = -6b + 1c Divide each side by '2'. a = -3b + 0.5c Simplifying a = -3b + 0.5c
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