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Simplifying 3(a + -1) + -1(3a + -4) = 3(2a + -2) + 19 Reorder the terms: 3(-1 + a) + -1(3a + -4) = 3(2a + -2) + 19 (-1 * 3 + a * 3) + -1(3a + -4) = 3(2a + -2) + 19 (-3 + 3a) + -1(3a + -4) = 3(2a + -2) + 19 Reorder the terms: -3 + 3a + -1(-4 + 3a) = 3(2a + -2) + 19 -3 + 3a + (-4 * -1 + 3a * -1) = 3(2a + -2) + 19 -3 + 3a + (4 + -3a) = 3(2a + -2) + 19 Reorder the terms: -3 + 4 + 3a + -3a = 3(2a + -2) + 19 Combine like terms: -3 + 4 = 1 1 + 3a + -3a = 3(2a + -2) + 19 Combine like terms: 3a + -3a = 0 1 + 0 = 3(2a + -2) + 19 1 = 3(2a + -2) + 19 Reorder the terms: 1 = 3(-2 + 2a) + 19 1 = (-2 * 3 + 2a * 3) + 19 1 = (-6 + 6a) + 19 Reorder the terms: 1 = -6 + 19 + 6a Combine like terms: -6 + 19 = 13 1 = 13 + 6a Solving 1 = 13 + 6a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6a' to each side of the equation. 1 + -6a = 13 + 6a + -6a Combine like terms: 6a + -6a = 0 1 + -6a = 13 + 0 1 + -6a = 13 Add '-1' to each side of the equation. 1 + -1 + -6a = 13 + -1 Combine like terms: 1 + -1 = 0 0 + -6a = 13 + -1 -6a = 13 + -1 Combine like terms: 13 + -1 = 12 -6a = 12 Divide each side by '-6'. a = -2 Simplifying a = -2
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