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Simplifying 5(4 + 2k) = 2(3k + -2) + -4(1 + k) (4 * 5 + 2k * 5) = 2(3k + -2) + -4(1 + k) (20 + 10k) = 2(3k + -2) + -4(1 + k) Reorder the terms: 20 + 10k = 2(-2 + 3k) + -4(1 + k) 20 + 10k = (-2 * 2 + 3k * 2) + -4(1 + k) 20 + 10k = (-4 + 6k) + -4(1 + k) 20 + 10k = -4 + 6k + (1 * -4 + k * -4) 20 + 10k = -4 + 6k + (-4 + -4k) Reorder the terms: 20 + 10k = -4 + -4 + 6k + -4k Combine like terms: -4 + -4 = -8 20 + 10k = -8 + 6k + -4k Combine like terms: 6k + -4k = 2k 20 + 10k = -8 + 2k Solving 20 + 10k = -8 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 20 + 10k + -2k = -8 + 2k + -2k Combine like terms: 10k + -2k = 8k 20 + 8k = -8 + 2k + -2k Combine like terms: 2k + -2k = 0 20 + 8k = -8 + 0 20 + 8k = -8 Add '-20' to each side of the equation. 20 + -20 + 8k = -8 + -20 Combine like terms: 20 + -20 = 0 0 + 8k = -8 + -20 8k = -8 + -20 Combine like terms: -8 + -20 = -28 8k = -28 Divide each side by '8'. k = -3.5 Simplifying k = -3.5
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