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Simplifying 8(x + 10) = 4(5 + 2x) + k Reorder the terms: 8(10 + x) = 4(5 + 2x) + k (10 * 8 + x * 8) = 4(5 + 2x) + k (80 + 8x) = 4(5 + 2x) + k 80 + 8x = (5 * 4 + 2x * 4) + k 80 + 8x = (20 + 8x) + k Reorder the terms: 80 + 8x = 20 + k + 8x Add '-8x' to each side of the equation. 80 + 8x + -8x = 20 + k + 8x + -8x Combine like terms: 8x + -8x = 0 80 + 0 = 20 + k + 8x + -8x 80 = 20 + k + 8x + -8x Combine like terms: 8x + -8x = 0 80 = 20 + k + 0 80 = 20 + k Solving 80 = 20 + k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1k' to each side of the equation. 80 + -1k = 20 + k + -1k Combine like terms: k + -1k = 0 80 + -1k = 20 + 0 80 + -1k = 20 Add '-80' to each side of the equation. 80 + -80 + -1k = 20 + -80 Combine like terms: 80 + -80 = 0 0 + -1k = 20 + -80 -1k = 20 + -80 Combine like terms: 20 + -80 = -60 -1k = -60 Divide each side by '-1'. k = 60 Simplifying k = 60
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