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Simplifying 10a + 3b + 12 = 8a + 8 + b Reorder the terms: 12 + 10a + 3b = 8a + 8 + b Reorder the terms: 12 + 10a + 3b = 8 + 8a + b Solving 12 + 10a + 3b = 8 + 8a + b Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8a' to each side of the equation. 12 + 10a + -8a + 3b = 8 + 8a + -8a + b Combine like terms: 10a + -8a = 2a 12 + 2a + 3b = 8 + 8a + -8a + b Combine like terms: 8a + -8a = 0 12 + 2a + 3b = 8 + 0 + b 12 + 2a + 3b = 8 + b Add '-12' to each side of the equation. 12 + 2a + -12 + 3b = 8 + -12 + b Reorder the terms: 12 + -12 + 2a + 3b = 8 + -12 + b Combine like terms: 12 + -12 = 0 0 + 2a + 3b = 8 + -12 + b 2a + 3b = 8 + -12 + b Combine like terms: 8 + -12 = -4 2a + 3b = -4 + b Add '-3b' to each side of the equation. 2a + 3b + -3b = -4 + b + -3b Combine like terms: 3b + -3b = 0 2a + 0 = -4 + b + -3b 2a = -4 + b + -3b Combine like terms: b + -3b = -2b 2a = -4 + -2b Divide each side by '2'. a = -2 + -1b Simplifying a = -2 + -1b
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