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Simplifying 4(2a + -3) + -2(a + -4) = 3(a + -3) + -1 Reorder the terms: 4(-3 + 2a) + -2(a + -4) = 3(a + -3) + -1 (-3 * 4 + 2a * 4) + -2(a + -4) = 3(a + -3) + -1 (-12 + 8a) + -2(a + -4) = 3(a + -3) + -1 Reorder the terms: -12 + 8a + -2(-4 + a) = 3(a + -3) + -1 -12 + 8a + (-4 * -2 + a * -2) = 3(a + -3) + -1 -12 + 8a + (8 + -2a) = 3(a + -3) + -1 Reorder the terms: -12 + 8 + 8a + -2a = 3(a + -3) + -1 Combine like terms: -12 + 8 = -4 -4 + 8a + -2a = 3(a + -3) + -1 Combine like terms: 8a + -2a = 6a -4 + 6a = 3(a + -3) + -1 Reorder the terms: -4 + 6a = 3(-3 + a) + -1 -4 + 6a = (-3 * 3 + a * 3) + -1 -4 + 6a = (-9 + 3a) + -1 Reorder the terms: -4 + 6a = -9 + -1 + 3a Combine like terms: -9 + -1 = -10 -4 + 6a = -10 + 3a Solving -4 + 6a = -10 + 3a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3a' to each side of the equation. -4 + 6a + -3a = -10 + 3a + -3a Combine like terms: 6a + -3a = 3a -4 + 3a = -10 + 3a + -3a Combine like terms: 3a + -3a = 0 -4 + 3a = -10 + 0 -4 + 3a = -10 Add '4' to each side of the equation. -4 + 4 + 3a = -10 + 4 Combine like terms: -4 + 4 = 0 0 + 3a = -10 + 4 3a = -10 + 4 Combine like terms: -10 + 4 = -6 3a = -6 Divide each side by '3'. a = -2 Simplifying a = -2
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