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Simplifying a + 5 + 7 = 3(4 + 6a) + -2(7a + 3) Reorder the terms: 5 + 7 + a = 3(4 + 6a) + -2(7a + 3) Combine like terms: 5 + 7 = 12 12 + a = 3(4 + 6a) + -2(7a + 3) 12 + a = (4 * 3 + 6a * 3) + -2(7a + 3) 12 + a = (12 + 18a) + -2(7a + 3) Reorder the terms: 12 + a = 12 + 18a + -2(3 + 7a) 12 + a = 12 + 18a + (3 * -2 + 7a * -2) 12 + a = 12 + 18a + (-6 + -14a) Reorder the terms: 12 + a = 12 + -6 + 18a + -14a Combine like terms: 12 + -6 = 6 12 + a = 6 + 18a + -14a Combine like terms: 18a + -14a = 4a 12 + a = 6 + 4a Solving 12 + a = 6 + 4a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4a' to each side of the equation. 12 + a + -4a = 6 + 4a + -4a Combine like terms: a + -4a = -3a 12 + -3a = 6 + 4a + -4a Combine like terms: 4a + -4a = 0 12 + -3a = 6 + 0 12 + -3a = 6 Add '-12' to each side of the equation. 12 + -12 + -3a = 6 + -12 Combine like terms: 12 + -12 = 0 0 + -3a = 6 + -12 -3a = 6 + -12 Combine like terms: 6 + -12 = -6 -3a = -6 Divide each side by '-3'. a = 2 Simplifying a = 2
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