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Simplifying 12k + -2(k + -11) = -4k + 10(k + 5) Reorder the terms: 12k + -2(-11 + k) = -4k + 10(k + 5) 12k + (-11 * -2 + k * -2) = -4k + 10(k + 5) 12k + (22 + -2k) = -4k + 10(k + 5) Reorder the terms: 22 + 12k + -2k = -4k + 10(k + 5) Combine like terms: 12k + -2k = 10k 22 + 10k = -4k + 10(k + 5) Reorder the terms: 22 + 10k = -4k + 10(5 + k) 22 + 10k = -4k + (5 * 10 + k * 10) 22 + 10k = -4k + (50 + 10k) Reorder the terms: 22 + 10k = 50 + -4k + 10k Combine like terms: -4k + 10k = 6k 22 + 10k = 50 + 6k Solving 22 + 10k = 50 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. 22 + 10k + -6k = 50 + 6k + -6k Combine like terms: 10k + -6k = 4k 22 + 4k = 50 + 6k + -6k Combine like terms: 6k + -6k = 0 22 + 4k = 50 + 0 22 + 4k = 50 Add '-22' to each side of the equation. 22 + -22 + 4k = 50 + -22 Combine like terms: 22 + -22 = 0 0 + 4k = 50 + -22 4k = 50 + -22 Combine like terms: 50 + -22 = 28 4k = 28 Divide each side by '4'. k = 7 Simplifying k = 7
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