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Simplifying -4(k + -10) + -2(1 + 8k) = -10k + 9k Reorder the terms: -4(-10 + k) + -2(1 + 8k) = -10k + 9k (-10 * -4 + k * -4) + -2(1 + 8k) = -10k + 9k (40 + -4k) + -2(1 + 8k) = -10k + 9k 40 + -4k + (1 * -2 + 8k * -2) = -10k + 9k 40 + -4k + (-2 + -16k) = -10k + 9k Reorder the terms: 40 + -2 + -4k + -16k = -10k + 9k Combine like terms: 40 + -2 = 38 38 + -4k + -16k = -10k + 9k Combine like terms: -4k + -16k = -20k 38 + -20k = -10k + 9k Combine like terms: -10k + 9k = -1k 38 + -20k = -1k Solving 38 + -20k = -1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add 'k' to each side of the equation. 38 + -20k + k = -1k + k Combine like terms: -20k + k = -19k 38 + -19k = -1k + k Combine like terms: -1k + k = 0 38 + -19k = 0 Add '-38' to each side of the equation. 38 + -38 + -19k = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -19k = 0 + -38 -19k = 0 + -38 Combine like terms: 0 + -38 = -38 -19k = -38 Divide each side by '-19'. k = 2 Simplifying k = 2
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