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Simplifying 8(k + -1) + 9(k + 3) + -2(k + -5) = 0 Reorder the terms: 8(-1 + k) + 9(k + 3) + -2(k + -5) = 0 (-1 * 8 + k * 8) + 9(k + 3) + -2(k + -5) = 0 (-8 + 8k) + 9(k + 3) + -2(k + -5) = 0 Reorder the terms: -8 + 8k + 9(3 + k) + -2(k + -5) = 0 -8 + 8k + (3 * 9 + k * 9) + -2(k + -5) = 0 -8 + 8k + (27 + 9k) + -2(k + -5) = 0 Reorder the terms: -8 + 8k + 27 + 9k + -2(-5 + k) = 0 -8 + 8k + 27 + 9k + (-5 * -2 + k * -2) = 0 -8 + 8k + 27 + 9k + (10 + -2k) = 0 Reorder the terms: -8 + 27 + 10 + 8k + 9k + -2k = 0 Combine like terms: -8 + 27 = 19 19 + 10 + 8k + 9k + -2k = 0 Combine like terms: 19 + 10 = 29 29 + 8k + 9k + -2k = 0 Combine like terms: 8k + 9k = 17k 29 + 17k + -2k = 0 Combine like terms: 17k + -2k = 15k 29 + 15k = 0 Solving 29 + 15k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 15k = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 15k = 0 + -29 15k = 0 + -29 Combine like terms: 0 + -29 = -29 15k = -29 Divide each side by '15'. k = -1.933333333 Simplifying k = -1.933333333
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