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Simplifying -1(-4k + 3) + -2(k + 4) = 5(k + -1) Reorder the terms: -1(3 + -4k) + -2(k + 4) = 5(k + -1) (3 * -1 + -4k * -1) + -2(k + 4) = 5(k + -1) (-3 + 4k) + -2(k + 4) = 5(k + -1) Reorder the terms: -3 + 4k + -2(4 + k) = 5(k + -1) -3 + 4k + (4 * -2 + k * -2) = 5(k + -1) -3 + 4k + (-8 + -2k) = 5(k + -1) Reorder the terms: -3 + -8 + 4k + -2k = 5(k + -1) Combine like terms: -3 + -8 = -11 -11 + 4k + -2k = 5(k + -1) Combine like terms: 4k + -2k = 2k -11 + 2k = 5(k + -1) Reorder the terms: -11 + 2k = 5(-1 + k) -11 + 2k = (-1 * 5 + k * 5) -11 + 2k = (-5 + 5k) Solving -11 + 2k = -5 + 5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5k' to each side of the equation. -11 + 2k + -5k = -5 + 5k + -5k Combine like terms: 2k + -5k = -3k -11 + -3k = -5 + 5k + -5k Combine like terms: 5k + -5k = 0 -11 + -3k = -5 + 0 -11 + -3k = -5 Add '11' to each side of the equation. -11 + 11 + -3k = -5 + 11 Combine like terms: -11 + 11 = 0 0 + -3k = -5 + 11 -3k = -5 + 11 Combine like terms: -5 + 11 = 6 -3k = 6 Divide each side by '-3'. k = -2 Simplifying k = -2
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