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Simplifying 10(k + 5) = 12(k + -2) Reorder the terms: 10(5 + k) = 12(k + -2) (5 * 10 + k * 10) = 12(k + -2) (50 + 10k) = 12(k + -2) Reorder the terms: 50 + 10k = 12(-2 + k) 50 + 10k = (-2 * 12 + k * 12) 50 + 10k = (-24 + 12k) Solving 50 + 10k = -24 + 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. 50 + 10k + -12k = -24 + 12k + -12k Combine like terms: 10k + -12k = -2k 50 + -2k = -24 + 12k + -12k Combine like terms: 12k + -12k = 0 50 + -2k = -24 + 0 50 + -2k = -24 Add '-50' to each side of the equation. 50 + -50 + -2k = -24 + -50 Combine like terms: 50 + -50 = 0 0 + -2k = -24 + -50 -2k = -24 + -50 Combine like terms: -24 + -50 = -74 -2k = -74 Divide each side by '-2'. k = 37 Simplifying k = 37
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