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Simplifying 8k + 7 + 1 + 3k = 7(3k + 4) + -3(-4 + -2k) Reorder the terms: 7 + 1 + 8k + 3k = 7(3k + 4) + -3(-4 + -2k) Combine like terms: 7 + 1 = 8 8 + 8k + 3k = 7(3k + 4) + -3(-4 + -2k) Combine like terms: 8k + 3k = 11k 8 + 11k = 7(3k + 4) + -3(-4 + -2k) Reorder the terms: 8 + 11k = 7(4 + 3k) + -3(-4 + -2k) 8 + 11k = (4 * 7 + 3k * 7) + -3(-4 + -2k) 8 + 11k = (28 + 21k) + -3(-4 + -2k) 8 + 11k = 28 + 21k + (-4 * -3 + -2k * -3) 8 + 11k = 28 + 21k + (12 + 6k) Reorder the terms: 8 + 11k = 28 + 12 + 21k + 6k Combine like terms: 28 + 12 = 40 8 + 11k = 40 + 21k + 6k Combine like terms: 21k + 6k = 27k 8 + 11k = 40 + 27k Solving 8 + 11k = 40 + 27k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-27k' to each side of the equation. 8 + 11k + -27k = 40 + 27k + -27k Combine like terms: 11k + -27k = -16k 8 + -16k = 40 + 27k + -27k Combine like terms: 27k + -27k = 0 8 + -16k = 40 + 0 8 + -16k = 40 Add '-8' to each side of the equation. 8 + -8 + -16k = 40 + -8 Combine like terms: 8 + -8 = 0 0 + -16k = 40 + -8 -16k = 40 + -8 Combine like terms: 40 + -8 = 32 -16k = 32 Divide each side by '-16'. k = -2 Simplifying k = -2
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