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Simplifying 64 = 8(1 + -7a) + -7(7 + 7a) 64 = (1 * 8 + -7a * 8) + -7(7 + 7a) 64 = (8 + -56a) + -7(7 + 7a) 64 = 8 + -56a + (7 * -7 + 7a * -7) 64 = 8 + -56a + (-49 + -49a) Reorder the terms: 64 = 8 + -49 + -56a + -49a Combine like terms: 8 + -49 = -41 64 = -41 + -56a + -49a Combine like terms: -56a + -49a = -105a 64 = -41 + -105a Solving 64 = -41 + -105a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '105a' to each side of the equation. 64 + 105a = -41 + -105a + 105a Combine like terms: -105a + 105a = 0 64 + 105a = -41 + 0 64 + 105a = -41 Add '-64' to each side of the equation. 64 + -64 + 105a = -41 + -64 Combine like terms: 64 + -64 = 0 0 + 105a = -41 + -64 105a = -41 + -64 Combine like terms: -41 + -64 = -105 105a = -105 Divide each side by '105'. a = -1 Simplifying a = -1
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