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Simplifying k + 8(-2k + -1 + -9) = -2k + -10(k + 10 + -2) Reorder the terms: k + 8(-1 + -9 + -2k) = -2k + -10(k + 10 + -2) Combine like terms: -1 + -9 = -10 k + 8(-10 + -2k) = -2k + -10(k + 10 + -2) k + (-10 * 8 + -2k * 8) = -2k + -10(k + 10 + -2) k + (-80 + -16k) = -2k + -10(k + 10 + -2) Reorder the terms: -80 + k + -16k = -2k + -10(k + 10 + -2) Combine like terms: k + -16k = -15k -80 + -15k = -2k + -10(k + 10 + -2) Reorder the terms: -80 + -15k = -2k + -10(10 + -2 + k) Combine like terms: 10 + -2 = 8 -80 + -15k = -2k + -10(8 + k) -80 + -15k = -2k + (8 * -10 + k * -10) -80 + -15k = -2k + (-80 + -10k) Reorder the terms: -80 + -15k = -80 + -2k + -10k Combine like terms: -2k + -10k = -12k -80 + -15k = -80 + -12k Add '80' to each side of the equation. -80 + 80 + -15k = -80 + 80 + -12k Combine like terms: -80 + 80 = 0 0 + -15k = -80 + 80 + -12k -15k = -80 + 80 + -12k Combine like terms: -80 + 80 = 0 -15k = 0 + -12k -15k = -12k Solving -15k = -12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '12k' to each side of the equation. -15k + 12k = -12k + 12k Combine like terms: -15k + 12k = -3k -3k = -12k + 12k Combine like terms: -12k + 12k = 0 -3k = 0 Divide each side by '-3'. k = 0 Simplifying k = 0
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