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Simplifying 3(a + -4) + -1(4a + -1) = 2(2a + -4) + 12 Reorder the terms: 3(-4 + a) + -1(4a + -1) = 2(2a + -4) + 12 (-4 * 3 + a * 3) + -1(4a + -1) = 2(2a + -4) + 12 (-12 + 3a) + -1(4a + -1) = 2(2a + -4) + 12 Reorder the terms: -12 + 3a + -1(-1 + 4a) = 2(2a + -4) + 12 -12 + 3a + (-1 * -1 + 4a * -1) = 2(2a + -4) + 12 -12 + 3a + (1 + -4a) = 2(2a + -4) + 12 Reorder the terms: -12 + 1 + 3a + -4a = 2(2a + -4) + 12 Combine like terms: -12 + 1 = -11 -11 + 3a + -4a = 2(2a + -4) + 12 Combine like terms: 3a + -4a = -1a -11 + -1a = 2(2a + -4) + 12 Reorder the terms: -11 + -1a = 2(-4 + 2a) + 12 -11 + -1a = (-4 * 2 + 2a * 2) + 12 -11 + -1a = (-8 + 4a) + 12 Reorder the terms: -11 + -1a = -8 + 12 + 4a Combine like terms: -8 + 12 = 4 -11 + -1a = 4 + 4a Solving -11 + -1a = 4 + 4a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4a' to each side of the equation. -11 + -1a + -4a = 4 + 4a + -4a Combine like terms: -1a + -4a = -5a -11 + -5a = 4 + 4a + -4a Combine like terms: 4a + -4a = 0 -11 + -5a = 4 + 0 -11 + -5a = 4 Add '11' to each side of the equation. -11 + 11 + -5a = 4 + 11 Combine like terms: -11 + 11 = 0 0 + -5a = 4 + 11 -5a = 4 + 11 Combine like terms: 4 + 11 = 15 -5a = 15 Divide each side by '-5'. a = -3 Simplifying a = -3
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