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Simplifying 4(4k + 2) + -8(k + -2) = 3(2k + 5) + -2 Reorder the terms: 4(2 + 4k) + -8(k + -2) = 3(2k + 5) + -2 (2 * 4 + 4k * 4) + -8(k + -2) = 3(2k + 5) + -2 (8 + 16k) + -8(k + -2) = 3(2k + 5) + -2 Reorder the terms: 8 + 16k + -8(-2 + k) = 3(2k + 5) + -2 8 + 16k + (-2 * -8 + k * -8) = 3(2k + 5) + -2 8 + 16k + (16 + -8k) = 3(2k + 5) + -2 Reorder the terms: 8 + 16 + 16k + -8k = 3(2k + 5) + -2 Combine like terms: 8 + 16 = 24 24 + 16k + -8k = 3(2k + 5) + -2 Combine like terms: 16k + -8k = 8k 24 + 8k = 3(2k + 5) + -2 Reorder the terms: 24 + 8k = 3(5 + 2k) + -2 24 + 8k = (5 * 3 + 2k * 3) + -2 24 + 8k = (15 + 6k) + -2 Reorder the terms: 24 + 8k = 15 + -2 + 6k Combine like terms: 15 + -2 = 13 24 + 8k = 13 + 6k Solving 24 + 8k = 13 + 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. 24 + 8k + -6k = 13 + 6k + -6k Combine like terms: 8k + -6k = 2k 24 + 2k = 13 + 6k + -6k Combine like terms: 6k + -6k = 0 24 + 2k = 13 + 0 24 + 2k = 13 Add '-24' to each side of the equation. 24 + -24 + 2k = 13 + -24 Combine like terms: 24 + -24 = 0 0 + 2k = 13 + -24 2k = 13 + -24 Combine like terms: 13 + -24 = -11 2k = -11 Divide each side by '2'. k = -5.5 Simplifying k = -5.5
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