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Simplifying (2 + -1a) * 4 = 5a + -1(2a + -3 + -8(1 + -1a)) Reorder the terms for easier multiplication: 4(2 + -1a) = 5a + -1(2a + -3 + -8(1 + -1a)) (2 * 4 + -1a * 4) = 5a + -1(2a + -3 + -8(1 + -1a)) (8 + -4a) = 5a + -1(2a + -3 + -8(1 + -1a)) 8 + -4a = 5a + -1(2a + -3 + (1 * -8 + -1a * -8)) 8 + -4a = 5a + -1(2a + -3 + (-8 + 8a)) Reorder the terms: 8 + -4a = 5a + -1(-3 + -8 + 2a + 8a) Combine like terms: -3 + -8 = -11 8 + -4a = 5a + -1(-11 + 2a + 8a) Combine like terms: 2a + 8a = 10a 8 + -4a = 5a + -1(-11 + 10a) 8 + -4a = 5a + (-11 * -1 + 10a * -1) 8 + -4a = 5a + (11 + -10a) Reorder the terms: 8 + -4a = 11 + 5a + -10a Combine like terms: 5a + -10a = -5a 8 + -4a = 11 + -5a Solving 8 + -4a = 11 + -5a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5a' to each side of the equation. 8 + -4a + 5a = 11 + -5a + 5a Combine like terms: -4a + 5a = 1a 8 + 1a = 11 + -5a + 5a Combine like terms: -5a + 5a = 0 8 + 1a = 11 + 0 8 + 1a = 11 Add '-8' to each side of the equation. 8 + -8 + 1a = 11 + -8 Combine like terms: 8 + -8 = 0 0 + 1a = 11 + -8 1a = 11 + -8 Combine like terms: 11 + -8 = 3 1a = 3 Divide each side by '1'. a = 3 Simplifying a = 3
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