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Simplifying -74 = 2(1 + 3a) + 8(1 + -6a) -74 = (1 * 2 + 3a * 2) + 8(1 + -6a) -74 = (2 + 6a) + 8(1 + -6a) -74 = 2 + 6a + (1 * 8 + -6a * 8) -74 = 2 + 6a + (8 + -48a) Reorder the terms: -74 = 2 + 8 + 6a + -48a Combine like terms: 2 + 8 = 10 -74 = 10 + 6a + -48a Combine like terms: 6a + -48a = -42a -74 = 10 + -42a Solving -74 = 10 + -42a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '42a' to each side of the equation. -74 + 42a = 10 + -42a + 42a Combine like terms: -42a + 42a = 0 -74 + 42a = 10 + 0 -74 + 42a = 10 Add '74' to each side of the equation. -74 + 74 + 42a = 10 + 74 Combine like terms: -74 + 74 = 0 0 + 42a = 10 + 74 42a = 10 + 74 Combine like terms: 10 + 74 = 84 42a = 84 Divide each side by '42'. a = 2 Simplifying a = 2
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