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Simplifying 5(a + 2) + 2(2a + -1) = 7(a + -4) Reorder the terms: 5(2 + a) + 2(2a + -1) = 7(a + -4) (2 * 5 + a * 5) + 2(2a + -1) = 7(a + -4) (10 + 5a) + 2(2a + -1) = 7(a + -4) Reorder the terms: 10 + 5a + 2(-1 + 2a) = 7(a + -4) 10 + 5a + (-1 * 2 + 2a * 2) = 7(a + -4) 10 + 5a + (-2 + 4a) = 7(a + -4) Reorder the terms: 10 + -2 + 5a + 4a = 7(a + -4) Combine like terms: 10 + -2 = 8 8 + 5a + 4a = 7(a + -4) Combine like terms: 5a + 4a = 9a 8 + 9a = 7(a + -4) Reorder the terms: 8 + 9a = 7(-4 + a) 8 + 9a = (-4 * 7 + a * 7) 8 + 9a = (-28 + 7a) Solving 8 + 9a = -28 + 7a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7a' to each side of the equation. 8 + 9a + -7a = -28 + 7a + -7a Combine like terms: 9a + -7a = 2a 8 + 2a = -28 + 7a + -7a Combine like terms: 7a + -7a = 0 8 + 2a = -28 + 0 8 + 2a = -28 Add '-8' to each side of the equation. 8 + -8 + 2a = -28 + -8 Combine like terms: 8 + -8 = 0 0 + 2a = -28 + -8 2a = -28 + -8 Combine like terms: -28 + -8 = -36 2a = -36 Divide each side by '2'. a = -18 Simplifying a = -18
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