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Simplifying (k + 3) + -1(5k + -3) = (3k + -11) + -1(k + 3) Reorder the terms: (3 + k) + -1(5k + -3) = (3k + -11) + -1(k + 3) Remove parenthesis around (3 + k) 3 + k + -1(5k + -3) = (3k + -11) + -1(k + 3) Reorder the terms: 3 + k + -1(-3 + 5k) = (3k + -11) + -1(k + 3) 3 + k + (-3 * -1 + 5k * -1) = (3k + -11) + -1(k + 3) 3 + k + (3 + -5k) = (3k + -11) + -1(k + 3) Reorder the terms: 3 + 3 + k + -5k = (3k + -11) + -1(k + 3) Combine like terms: 3 + 3 = 6 6 + k + -5k = (3k + -11) + -1(k + 3) Combine like terms: k + -5k = -4k 6 + -4k = (3k + -11) + -1(k + 3) Reorder the terms: 6 + -4k = (-11 + 3k) + -1(k + 3) Remove parenthesis around (-11 + 3k) 6 + -4k = -11 + 3k + -1(k + 3) Reorder the terms: 6 + -4k = -11 + 3k + -1(3 + k) 6 + -4k = -11 + 3k + (3 * -1 + k * -1) 6 + -4k = -11 + 3k + (-3 + -1k) Reorder the terms: 6 + -4k = -11 + -3 + 3k + -1k Combine like terms: -11 + -3 = -14 6 + -4k = -14 + 3k + -1k Combine like terms: 3k + -1k = 2k 6 + -4k = -14 + 2k Solving 6 + -4k = -14 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 6 + -4k + -2k = -14 + 2k + -2k Combine like terms: -4k + -2k = -6k 6 + -6k = -14 + 2k + -2k Combine like terms: 2k + -2k = 0 6 + -6k = -14 + 0 6 + -6k = -14 Add '-6' to each side of the equation. 6 + -6 + -6k = -14 + -6 Combine like terms: 6 + -6 = 0 0 + -6k = -14 + -6 -6k = -14 + -6 Combine like terms: -14 + -6 = -20 -6k = -20 Divide each side by '-6'. k = 3.333333333 Simplifying k = 3.333333333
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