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Simplifying 45 + -1(3k + -13) + 10 + -5(k + 1) = 0 Reorder the terms: 45 + -1(-13 + 3k) + 10 + -5(k + 1) = 0 45 + (-13 * -1 + 3k * -1) + 10 + -5(k + 1) = 0 45 + (13 + -3k) + 10 + -5(k + 1) = 0 Reorder the terms: 45 + 13 + -3k + 10 + -5(1 + k) = 0 45 + 13 + -3k + 10 + (1 * -5 + k * -5) = 0 45 + 13 + -3k + 10 + (-5 + -5k) = 0 Reorder the terms: 45 + 13 + 10 + -5 + -3k + -5k = 0 Combine like terms: 45 + 13 = 58 58 + 10 + -5 + -3k + -5k = 0 Combine like terms: 58 + 10 = 68 68 + -5 + -3k + -5k = 0 Combine like terms: 68 + -5 = 63 63 + -3k + -5k = 0 Combine like terms: -3k + -5k = -8k 63 + -8k = 0 Solving 63 + -8k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-63' to each side of the equation. 63 + -63 + -8k = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -8k = 0 + -63 -8k = 0 + -63 Combine like terms: 0 + -63 = -63 -8k = -63 Divide each side by '-8'. k = 7.875 Simplifying k = 7.875
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