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Simplifying 3(9 + 5r) + -8(1 + k) = 0 (9 * 3 + 5r * 3) + -8(1 + k) = 0 (27 + 15r) + -8(1 + k) = 0 27 + 15r + (1 * -8 + k * -8) = 0 27 + 15r + (-8 + -8k) = 0 Reorder the terms: 27 + -8 + -8k + 15r = 0 Combine like terms: 27 + -8 = 19 19 + -8k + 15r = 0 Solving 19 + -8k + 15r = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -8k + -19 + 15r = 0 + -19 Reorder the terms: 19 + -19 + -8k + 15r = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -8k + 15r = 0 + -19 -8k + 15r = 0 + -19 Combine like terms: 0 + -19 = -19 -8k + 15r = -19 Add '-15r' to each side of the equation. -8k + 15r + -15r = -19 + -15r Combine like terms: 15r + -15r = 0 -8k + 0 = -19 + -15r -8k = -19 + -15r Divide each side by '-8'. k = 2.375 + 1.875r Simplifying k = 2.375 + 1.875r
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