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Simplifying 4(1 + -2k) + 3k = -5k + -4(k + 1) (1 * 4 + -2k * 4) + 3k = -5k + -4(k + 1) (4 + -8k) + 3k = -5k + -4(k + 1) Combine like terms: -8k + 3k = -5k 4 + -5k = -5k + -4(k + 1) Reorder the terms: 4 + -5k = -5k + -4(1 + k) 4 + -5k = -5k + (1 * -4 + k * -4) 4 + -5k = -5k + (-4 + -4k) Reorder the terms: 4 + -5k = -4 + -5k + -4k Combine like terms: -5k + -4k = -9k 4 + -5k = -4 + -9k Solving 4 + -5k = -4 + -9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9k' to each side of the equation. 4 + -5k + 9k = -4 + -9k + 9k Combine like terms: -5k + 9k = 4k 4 + 4k = -4 + -9k + 9k Combine like terms: -9k + 9k = 0 4 + 4k = -4 + 0 4 + 4k = -4 Add '-4' to each side of the equation. 4 + -4 + 4k = -4 + -4 Combine like terms: 4 + -4 = 0 0 + 4k = -4 + -4 4k = -4 + -4 Combine like terms: -4 + -4 = -8 4k = -8 Divide each side by '4'. k = -2 Simplifying k = -2
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