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Simplifying 7(6 + -2a) = 5(-3a + 1) + 8 (6 * 7 + -2a * 7) = 5(-3a + 1) + 8 (42 + -14a) = 5(-3a + 1) + 8 Reorder the terms: 42 + -14a = 5(1 + -3a) + 8 42 + -14a = (1 * 5 + -3a * 5) + 8 42 + -14a = (5 + -15a) + 8 Reorder the terms: 42 + -14a = 5 + 8 + -15a Combine like terms: 5 + 8 = 13 42 + -14a = 13 + -15a Solving 42 + -14a = 13 + -15a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15a' to each side of the equation. 42 + -14a + 15a = 13 + -15a + 15a Combine like terms: -14a + 15a = 1a 42 + 1a = 13 + -15a + 15a Combine like terms: -15a + 15a = 0 42 + 1a = 13 + 0 42 + 1a = 13 Add '-42' to each side of the equation. 42 + -42 + 1a = 13 + -42 Combine like terms: 42 + -42 = 0 0 + 1a = 13 + -42 1a = 13 + -42 Combine like terms: 13 + -42 = -29 1a = -29 Divide each side by '1'. a = -29 Simplifying a = -29
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