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Simplifying 61a + 5 = 2(a + 3) + 6(a + 1) Reorder the terms: 5 + 61a = 2(a + 3) + 6(a + 1) Reorder the terms: 5 + 61a = 2(3 + a) + 6(a + 1) 5 + 61a = (3 * 2 + a * 2) + 6(a + 1) 5 + 61a = (6 + 2a) + 6(a + 1) Reorder the terms: 5 + 61a = 6 + 2a + 6(1 + a) 5 + 61a = 6 + 2a + (1 * 6 + a * 6) 5 + 61a = 6 + 2a + (6 + 6a) Reorder the terms: 5 + 61a = 6 + 6 + 2a + 6a Combine like terms: 6 + 6 = 12 5 + 61a = 12 + 2a + 6a Combine like terms: 2a + 6a = 8a 5 + 61a = 12 + 8a Solving 5 + 61a = 12 + 8a 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. 5 + 61a + -8a = 12 + 8a + -8a Combine like terms: 61a + -8a = 53a 5 + 53a = 12 + 8a + -8a Combine like terms: 8a + -8a = 0 5 + 53a = 12 + 0 5 + 53a = 12 Add '-5' to each side of the equation. 5 + -5 + 53a = 12 + -5 Combine like terms: 5 + -5 = 0 0 + 53a = 12 + -5 53a = 12 + -5 Combine like terms: 12 + -5 = 7 53a = 7 Divide each side by '53'. a = 0.1320754717 Simplifying a = 0.1320754717
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