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Simplifying 8(5 + -3k) = -1(k + 7) + 1 (5 * 8 + -3k * 8) = -1(k + 7) + 1 (40 + -24k) = -1(k + 7) + 1 Reorder the terms: 40 + -24k = -1(7 + k) + 1 40 + -24k = (7 * -1 + k * -1) + 1 40 + -24k = (-7 + -1k) + 1 Reorder the terms: 40 + -24k = -7 + 1 + -1k Combine like terms: -7 + 1 = -6 40 + -24k = -6 + -1k Solving 40 + -24k = -6 + -1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add 'k' to each side of the equation. 40 + -24k + k = -6 + -1k + k Combine like terms: -24k + k = -23k 40 + -23k = -6 + -1k + k Combine like terms: -1k + k = 0 40 + -23k = -6 + 0 40 + -23k = -6 Add '-40' to each side of the equation. 40 + -40 + -23k = -6 + -40 Combine like terms: 40 + -40 = 0 0 + -23k = -6 + -40 -23k = -6 + -40 Combine like terms: -6 + -40 = -46 -23k = -46 Divide each side by '-23'. k = 2 Simplifying k = 2
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