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Simplifying -10(k + 5) = 8(k + 4) + 8 Reorder the terms: -10(5 + k) = 8(k + 4) + 8 (5 * -10 + k * -10) = 8(k + 4) + 8 (-50 + -10k) = 8(k + 4) + 8 Reorder the terms: -50 + -10k = 8(4 + k) + 8 -50 + -10k = (4 * 8 + k * 8) + 8 -50 + -10k = (32 + 8k) + 8 Reorder the terms: -50 + -10k = 32 + 8 + 8k Combine like terms: 32 + 8 = 40 -50 + -10k = 40 + 8k Solving -50 + -10k = 40 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. -50 + -10k + -8k = 40 + 8k + -8k Combine like terms: -10k + -8k = -18k -50 + -18k = 40 + 8k + -8k Combine like terms: 8k + -8k = 0 -50 + -18k = 40 + 0 -50 + -18k = 40 Add '50' to each side of the equation. -50 + 50 + -18k = 40 + 50 Combine like terms: -50 + 50 = 0 0 + -18k = 40 + 50 -18k = 40 + 50 Combine like terms: 40 + 50 = 90 -18k = 90 Divide each side by '-18'. k = -5 Simplifying k = -5
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