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Simplifying 3(a + -4) + 5(a + -2) = 2(a + -6) + -4(5 + -1a) Reorder the terms: 3(-4 + a) + 5(a + -2) = 2(a + -6) + -4(5 + -1a) (-4 * 3 + a * 3) + 5(a + -2) = 2(a + -6) + -4(5 + -1a) (-12 + 3a) + 5(a + -2) = 2(a + -6) + -4(5 + -1a) Reorder the terms: -12 + 3a + 5(-2 + a) = 2(a + -6) + -4(5 + -1a) -12 + 3a + (-2 * 5 + a * 5) = 2(a + -6) + -4(5 + -1a) -12 + 3a + (-10 + 5a) = 2(a + -6) + -4(5 + -1a) Reorder the terms: -12 + -10 + 3a + 5a = 2(a + -6) + -4(5 + -1a) Combine like terms: -12 + -10 = -22 -22 + 3a + 5a = 2(a + -6) + -4(5 + -1a) Combine like terms: 3a + 5a = 8a -22 + 8a = 2(a + -6) + -4(5 + -1a) Reorder the terms: -22 + 8a = 2(-6 + a) + -4(5 + -1a) -22 + 8a = (-6 * 2 + a * 2) + -4(5 + -1a) -22 + 8a = (-12 + 2a) + -4(5 + -1a) -22 + 8a = -12 + 2a + (5 * -4 + -1a * -4) -22 + 8a = -12 + 2a + (-20 + 4a) Reorder the terms: -22 + 8a = -12 + -20 + 2a + 4a Combine like terms: -12 + -20 = -32 -22 + 8a = -32 + 2a + 4a Combine like terms: 2a + 4a = 6a -22 + 8a = -32 + 6a Solving -22 + 8a = -32 + 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. -22 + 8a + -6a = -32 + 6a + -6a Combine like terms: 8a + -6a = 2a -22 + 2a = -32 + 6a + -6a Combine like terms: 6a + -6a = 0 -22 + 2a = -32 + 0 -22 + 2a = -32 Add '22' to each side of the equation. -22 + 22 + 2a = -32 + 22 Combine like terms: -22 + 22 = 0 0 + 2a = -32 + 22 2a = -32 + 22 Combine like terms: -32 + 22 = -10 2a = -10 Divide each side by '2'. a = -5 Simplifying a = -5
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