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Simplifying a + 8 + 1 + 4a = 2(4a + 3) + 4(a + 6) Reorder the terms: 8 + 1 + a + 4a = 2(4a + 3) + 4(a + 6) Combine like terms: 8 + 1 = 9 9 + a + 4a = 2(4a + 3) + 4(a + 6) Combine like terms: a + 4a = 5a 9 + 5a = 2(4a + 3) + 4(a + 6) Reorder the terms: 9 + 5a = 2(3 + 4a) + 4(a + 6) 9 + 5a = (3 * 2 + 4a * 2) + 4(a + 6) 9 + 5a = (6 + 8a) + 4(a + 6) Reorder the terms: 9 + 5a = 6 + 8a + 4(6 + a) 9 + 5a = 6 + 8a + (6 * 4 + a * 4) 9 + 5a = 6 + 8a + (24 + 4a) Reorder the terms: 9 + 5a = 6 + 24 + 8a + 4a Combine like terms: 6 + 24 = 30 9 + 5a = 30 + 8a + 4a Combine like terms: 8a + 4a = 12a 9 + 5a = 30 + 12a Solving 9 + 5a = 30 + 12a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12a' to each side of the equation. 9 + 5a + -12a = 30 + 12a + -12a Combine like terms: 5a + -12a = -7a 9 + -7a = 30 + 12a + -12a Combine like terms: 12a + -12a = 0 9 + -7a = 30 + 0 9 + -7a = 30 Add '-9' to each side of the equation. 9 + -9 + -7a = 30 + -9 Combine like terms: 9 + -9 = 0 0 + -7a = 30 + -9 -7a = 30 + -9 Combine like terms: 30 + -9 = 21 -7a = 21 Divide each side by '-7'. a = -3 Simplifying a = -3
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