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Simplifying 6(5a + 3) + -3(2a + -4) = 7(a + 9) + 3(5a + -6) Reorder the terms: 6(3 + 5a) + -3(2a + -4) = 7(a + 9) + 3(5a + -6) (3 * 6 + 5a * 6) + -3(2a + -4) = 7(a + 9) + 3(5a + -6) (18 + 30a) + -3(2a + -4) = 7(a + 9) + 3(5a + -6) Reorder the terms: 18 + 30a + -3(-4 + 2a) = 7(a + 9) + 3(5a + -6) 18 + 30a + (-4 * -3 + 2a * -3) = 7(a + 9) + 3(5a + -6) 18 + 30a + (12 + -6a) = 7(a + 9) + 3(5a + -6) Reorder the terms: 18 + 12 + 30a + -6a = 7(a + 9) + 3(5a + -6) Combine like terms: 18 + 12 = 30 30 + 30a + -6a = 7(a + 9) + 3(5a + -6) Combine like terms: 30a + -6a = 24a 30 + 24a = 7(a + 9) + 3(5a + -6) Reorder the terms: 30 + 24a = 7(9 + a) + 3(5a + -6) 30 + 24a = (9 * 7 + a * 7) + 3(5a + -6) 30 + 24a = (63 + 7a) + 3(5a + -6) Reorder the terms: 30 + 24a = 63 + 7a + 3(-6 + 5a) 30 + 24a = 63 + 7a + (-6 * 3 + 5a * 3) 30 + 24a = 63 + 7a + (-18 + 15a) Reorder the terms: 30 + 24a = 63 + -18 + 7a + 15a Combine like terms: 63 + -18 = 45 30 + 24a = 45 + 7a + 15a Combine like terms: 7a + 15a = 22a 30 + 24a = 45 + 22a Solving 30 + 24a = 45 + 22a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-22a' to each side of the equation. 30 + 24a + -22a = 45 + 22a + -22a Combine like terms: 24a + -22a = 2a 30 + 2a = 45 + 22a + -22a Combine like terms: 22a + -22a = 0 30 + 2a = 45 + 0 30 + 2a = 45 Add '-30' to each side of the equation. 30 + -30 + 2a = 45 + -30 Combine like terms: 30 + -30 = 0 0 + 2a = 45 + -30 2a = 45 + -30 Combine like terms: 45 + -30 = 15 2a = 15 Divide each side by '2'. a = 7.5 Simplifying a = 7.5
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