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Simplifying -51 = -7(-1 + 4a) + 5(1 + -7a) -51 = (-1 * -7 + 4a * -7) + 5(1 + -7a) -51 = (7 + -28a) + 5(1 + -7a) -51 = 7 + -28a + (1 * 5 + -7a * 5) -51 = 7 + -28a + (5 + -35a) Reorder the terms: -51 = 7 + 5 + -28a + -35a Combine like terms: 7 + 5 = 12 -51 = 12 + -28a + -35a Combine like terms: -28a + -35a = -63a -51 = 12 + -63a Solving -51 = 12 + -63a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '63a' to each side of the equation. -51 + 63a = 12 + -63a + 63a Combine like terms: -63a + 63a = 0 -51 + 63a = 12 + 0 -51 + 63a = 12 Add '51' to each side of the equation. -51 + 51 + 63a = 12 + 51 Combine like terms: -51 + 51 = 0 0 + 63a = 12 + 51 63a = 12 + 51 Combine like terms: 12 + 51 = 63 63a = 63 Divide each side by '63'. a = 1 Simplifying a = 1
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