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Simplifying 5 = 7(4 + a) + -1(1 + -4a) 5 = (4 * 7 + a * 7) + -1(1 + -4a) 5 = (28 + 7a) + -1(1 + -4a) 5 = 28 + 7a + (1 * -1 + -4a * -1) 5 = 28 + 7a + (-1 + 4a) Reorder the terms: 5 = 28 + -1 + 7a + 4a Combine like terms: 28 + -1 = 27 5 = 27 + 7a + 4a Combine like terms: 7a + 4a = 11a 5 = 27 + 11a Solving 5 = 27 + 11a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-11a' to each side of the equation. 5 + -11a = 27 + 11a + -11a Combine like terms: 11a + -11a = 0 5 + -11a = 27 + 0 5 + -11a = 27 Add '-5' to each side of the equation. 5 + -5 + -11a = 27 + -5 Combine like terms: 5 + -5 = 0 0 + -11a = 27 + -5 -11a = 27 + -5 Combine like terms: 27 + -5 = 22 -11a = 22 Divide each side by '-11'. a = -2 Simplifying a = -2
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