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Simplifying 9 = 8(a + 4) + 5(1 + 4a) Reorder the terms: 9 = 8(4 + a) + 5(1 + 4a) 9 = (4 * 8 + a * 8) + 5(1 + 4a) 9 = (32 + 8a) + 5(1 + 4a) 9 = 32 + 8a + (1 * 5 + 4a * 5) 9 = 32 + 8a + (5 + 20a) Reorder the terms: 9 = 32 + 5 + 8a + 20a Combine like terms: 32 + 5 = 37 9 = 37 + 8a + 20a Combine like terms: 8a + 20a = 28a 9 = 37 + 28a Solving 9 = 37 + 28a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-28a' to each side of the equation. 9 + -28a = 37 + 28a + -28a Combine like terms: 28a + -28a = 0 9 + -28a = 37 + 0 9 + -28a = 37 Add '-9' to each side of the equation. 9 + -9 + -28a = 37 + -9 Combine like terms: 9 + -9 = 0 0 + -28a = 37 + -9 -28a = 37 + -9 Combine like terms: 37 + -9 = 28 -28a = 28 Divide each side by '-28'. a = -1 Simplifying a = -1
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