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Simplifying 4a + -1(6 + -5a) + 12 = 3a + 2(2a + -4) 4a + (6 * -1 + -5a * -1) + 12 = 3a + 2(2a + -4) 4a + (-6 + 5a) + 12 = 3a + 2(2a + -4) Reorder the terms: -6 + 12 + 4a + 5a = 3a + 2(2a + -4) Combine like terms: -6 + 12 = 6 6 + 4a + 5a = 3a + 2(2a + -4) Combine like terms: 4a + 5a = 9a 6 + 9a = 3a + 2(2a + -4) Reorder the terms: 6 + 9a = 3a + 2(-4 + 2a) 6 + 9a = 3a + (-4 * 2 + 2a * 2) 6 + 9a = 3a + (-8 + 4a) Reorder the terms: 6 + 9a = -8 + 3a + 4a Combine like terms: 3a + 4a = 7a 6 + 9a = -8 + 7a Solving 6 + 9a = -8 + 7a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7a' to each side of the equation. 6 + 9a + -7a = -8 + 7a + -7a Combine like terms: 9a + -7a = 2a 6 + 2a = -8 + 7a + -7a Combine like terms: 7a + -7a = 0 6 + 2a = -8 + 0 6 + 2a = -8 Add '-6' to each side of the equation. 6 + -6 + 2a = -8 + -6 Combine like terms: 6 + -6 = 0 0 + 2a = -8 + -6 2a = -8 + -6 Combine like terms: -8 + -6 = -14 2a = -14 Divide each side by '2'. a = -7 Simplifying a = -7
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