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Simplifying k + 9(-2k + 19) = 14k + -16 + -20k Reorder the terms: k + 9(19 + -2k) = 14k + -16 + -20k k + (19 * 9 + -2k * 9) = 14k + -16 + -20k k + (171 + -18k) = 14k + -16 + -20k Reorder the terms: 171 + k + -18k = 14k + -16 + -20k Combine like terms: k + -18k = -17k 171 + -17k = 14k + -16 + -20k Reorder the terms: 171 + -17k = -16 + 14k + -20k Combine like terms: 14k + -20k = -6k 171 + -17k = -16 + -6k Solving 171 + -17k = -16 + -6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6k' to each side of the equation. 171 + -17k + 6k = -16 + -6k + 6k Combine like terms: -17k + 6k = -11k 171 + -11k = -16 + -6k + 6k Combine like terms: -6k + 6k = 0 171 + -11k = -16 + 0 171 + -11k = -16 Add '-171' to each side of the equation. 171 + -171 + -11k = -16 + -171 Combine like terms: 171 + -171 = 0 0 + -11k = -16 + -171 -11k = -16 + -171 Combine like terms: -16 + -171 = -187 -11k = -187 Divide each side by '-11'. k = 17 Simplifying k = 17
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