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Simplifying 3a + 4b + -5c = 2a + -3b + 4c Solving 3a + 4b + -5c = 2a + -3b + 4c Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2a' to each side of the equation. 3a + 4b + -2a + -5c = 2a + -3b + -2a + 4c Reorder the terms: 3a + -2a + 4b + -5c = 2a + -3b + -2a + 4c Combine like terms: 3a + -2a = 1a 1a + 4b + -5c = 2a + -3b + -2a + 4c Reorder the terms: 1a + 4b + -5c = 2a + -2a + -3b + 4c Combine like terms: 2a + -2a = 0 1a + 4b + -5c = 0 + -3b + 4c 1a + 4b + -5c = -3b + 4c Add '-4b' to each side of the equation. 1a + 4b + -4b + -5c = -3b + -4b + 4c Combine like terms: 4b + -4b = 0 1a + 0 + -5c = -3b + -4b + 4c 1a + -5c = -3b + -4b + 4c Combine like terms: -3b + -4b = -7b 1a + -5c = -7b + 4c Add '5c' to each side of the equation. 1a + -5c + 5c = -7b + 4c + 5c Combine like terms: -5c + 5c = 0 1a + 0 = -7b + 4c + 5c 1a = -7b + 4c + 5c Combine like terms: 4c + 5c = 9c 1a = -7b + 9c Divide each side by '1'. a = -7b + 9c Simplifying a = -7b + 9c
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