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Simplifying 5k + 9 + k + -1 = 8(k + -8) + 2(2k + -6) Reorder the terms: 9 + -1 + 5k + k = 8(k + -8) + 2(2k + -6) Combine like terms: 9 + -1 = 8 8 + 5k + k = 8(k + -8) + 2(2k + -6) Combine like terms: 5k + k = 6k 8 + 6k = 8(k + -8) + 2(2k + -6) Reorder the terms: 8 + 6k = 8(-8 + k) + 2(2k + -6) 8 + 6k = (-8 * 8 + k * 8) + 2(2k + -6) 8 + 6k = (-64 + 8k) + 2(2k + -6) Reorder the terms: 8 + 6k = -64 + 8k + 2(-6 + 2k) 8 + 6k = -64 + 8k + (-6 * 2 + 2k * 2) 8 + 6k = -64 + 8k + (-12 + 4k) Reorder the terms: 8 + 6k = -64 + -12 + 8k + 4k Combine like terms: -64 + -12 = -76 8 + 6k = -76 + 8k + 4k Combine like terms: 8k + 4k = 12k 8 + 6k = -76 + 12k Solving 8 + 6k = -76 + 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. 8 + 6k + -12k = -76 + 12k + -12k Combine like terms: 6k + -12k = -6k 8 + -6k = -76 + 12k + -12k Combine like terms: 12k + -12k = 0 8 + -6k = -76 + 0 8 + -6k = -76 Add '-8' to each side of the equation. 8 + -8 + -6k = -76 + -8 Combine like terms: 8 + -8 = 0 0 + -6k = -76 + -8 -6k = -76 + -8 Combine like terms: -76 + -8 = -84 -6k = -84 Divide each side by '-6'. k = 14 Simplifying k = 14
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