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Simplifying -65 = 5(k + 6) + -3(1 + -6k) Reorder the terms: -65 = 5(6 + k) + -3(1 + -6k) -65 = (6 * 5 + k * 5) + -3(1 + -6k) -65 = (30 + 5k) + -3(1 + -6k) -65 = 30 + 5k + (1 * -3 + -6k * -3) -65 = 30 + 5k + (-3 + 18k) Reorder the terms: -65 = 30 + -3 + 5k + 18k Combine like terms: 30 + -3 = 27 -65 = 27 + 5k + 18k Combine like terms: 5k + 18k = 23k -65 = 27 + 23k Solving -65 = 27 + 23k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-23k' to each side of the equation. -65 + -23k = 27 + 23k + -23k Combine like terms: 23k + -23k = 0 -65 + -23k = 27 + 0 -65 + -23k = 27 Add '65' to each side of the equation. -65 + 65 + -23k = 27 + 65 Combine like terms: -65 + 65 = 0 0 + -23k = 27 + 65 -23k = 27 + 65 Combine like terms: 27 + 65 = 92 -23k = 92 Divide each side by '-23'. k = -4 Simplifying k = -4
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