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Simplifying 12a + 6(4 + -7c) = 9(2a + 4) 12a + (4 * 6 + -7c * 6) = 9(2a + 4) 12a + (24 + -42c) = 9(2a + 4) Reorder the terms: 24 + 12a + -42c = 9(2a + 4) Reorder the terms: 24 + 12a + -42c = 9(4 + 2a) 24 + 12a + -42c = (4 * 9 + 2a * 9) 24 + 12a + -42c = (36 + 18a) Solving 24 + 12a + -42c = 36 + 18a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-18a' to each side of the equation. 24 + 12a + -18a + -42c = 36 + 18a + -18a Combine like terms: 12a + -18a = -6a 24 + -6a + -42c = 36 + 18a + -18a Combine like terms: 18a + -18a = 0 24 + -6a + -42c = 36 + 0 24 + -6a + -42c = 36 Add '-24' to each side of the equation. 24 + -6a + -24 + -42c = 36 + -24 Reorder the terms: 24 + -24 + -6a + -42c = 36 + -24 Combine like terms: 24 + -24 = 0 0 + -6a + -42c = 36 + -24 -6a + -42c = 36 + -24 Combine like terms: 36 + -24 = 12 -6a + -42c = 12 Add '42c' to each side of the equation. -6a + -42c + 42c = 12 + 42c Combine like terms: -42c + 42c = 0 -6a + 0 = 12 + 42c -6a = 12 + 42c Divide each side by '-6'. a = -2 + -7c Simplifying a = -2 + -7c
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