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Simplifying 2k + -2(1 + 4k) = 8(5 + k) 2k + (1 * -2 + 4k * -2) = 8(5 + k) 2k + (-2 + -8k) = 8(5 + k) Reorder the terms: -2 + 2k + -8k = 8(5 + k) Combine like terms: 2k + -8k = -6k -2 + -6k = 8(5 + k) -2 + -6k = (5 * 8 + k * 8) -2 + -6k = (40 + 8k) Solving -2 + -6k = 40 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. -2 + -6k + -8k = 40 + 8k + -8k Combine like terms: -6k + -8k = -14k -2 + -14k = 40 + 8k + -8k Combine like terms: 8k + -8k = 0 -2 + -14k = 40 + 0 -2 + -14k = 40 Add '2' to each side of the equation. -2 + 2 + -14k = 40 + 2 Combine like terms: -2 + 2 = 0 0 + -14k = 40 + 2 -14k = 40 + 2 Combine like terms: 40 + 2 = 42 -14k = 42 Divide each side by '-14'. k = -3 Simplifying k = -3
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