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Simplifying 51 = -6(1 + 2a) + -5(-1 + 8a) 51 = (1 * -6 + 2a * -6) + -5(-1 + 8a) 51 = (-6 + -12a) + -5(-1 + 8a) 51 = -6 + -12a + (-1 * -5 + 8a * -5) 51 = -6 + -12a + (5 + -40a) Reorder the terms: 51 = -6 + 5 + -12a + -40a Combine like terms: -6 + 5 = -1 51 = -1 + -12a + -40a Combine like terms: -12a + -40a = -52a 51 = -1 + -52a Solving 51 = -1 + -52a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '52a' to each side of the equation. 51 + 52a = -1 + -52a + 52a Combine like terms: -52a + 52a = 0 51 + 52a = -1 + 0 51 + 52a = -1 Add '-51' to each side of the equation. 51 + -51 + 52a = -1 + -51 Combine like terms: 51 + -51 = 0 0 + 52a = -1 + -51 52a = -1 + -51 Combine like terms: -1 + -51 = -52 52a = -52 Divide each side by '52'. a = -1 Simplifying a = -1
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