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Simplifying 13(65a + 40) = 52(-8a + 204) Reorder the terms: 13(40 + 65a) = 52(-8a + 204) (40 * 13 + 65a * 13) = 52(-8a + 204) (520 + 845a) = 52(-8a + 204) Reorder the terms: 520 + 845a = 52(204 + -8a) 520 + 845a = (204 * 52 + -8a * 52) 520 + 845a = (10608 + -416a) Solving 520 + 845a = 10608 + -416a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '416a' to each side of the equation. 520 + 845a + 416a = 10608 + -416a + 416a Combine like terms: 845a + 416a = 1261a 520 + 1261a = 10608 + -416a + 416a Combine like terms: -416a + 416a = 0 520 + 1261a = 10608 + 0 520 + 1261a = 10608 Add '-520' to each side of the equation. 520 + -520 + 1261a = 10608 + -520 Combine like terms: 520 + -520 = 0 0 + 1261a = 10608 + -520 1261a = 10608 + -520 Combine like terms: 10608 + -520 = 10088 1261a = 10088 Divide each side by '1261'. a = 8 Simplifying a = 8
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