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Simplifying a + 3 + (3a + -1b) = 6 + 6i Remove parenthesis around (3a + -1b) a + 3 + 3a + -1b = 6 + 6i Reorder the terms: 3 + a + 3a + -1b = 6 + 6i Combine like terms: a + 3a = 4a 3 + 4a + -1b = 6 + 6i Solving 3 + 4a + -1b = 6 + 6i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + 4a + -3 + -1b = 6 + -3 + 6i Reorder the terms: 3 + -3 + 4a + -1b = 6 + -3 + 6i Combine like terms: 3 + -3 = 0 0 + 4a + -1b = 6 + -3 + 6i 4a + -1b = 6 + -3 + 6i Combine like terms: 6 + -3 = 3 4a + -1b = 3 + 6i Add 'b' to each side of the equation. 4a + -1b + b = 3 + b + 6i Combine like terms: -1b + b = 0 4a + 0 = 3 + b + 6i 4a = 3 + b + 6i Divide each side by '4'. a = 0.75 + 0.25b + 1.5i Simplifying a = 0.75 + 0.25b + 1.5i
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