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Simplifying -82 = k + -7(1 + -2k) -82 = k + (1 * -7 + -2k * -7) -82 = k + (-7 + 14k) Reorder the terms: -82 = -7 + k + 14k Combine like terms: k + 14k = 15k -82 = -7 + 15k Solving -82 = -7 + 15k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-15k' to each side of the equation. -82 + -15k = -7 + 15k + -15k Combine like terms: 15k + -15k = 0 -82 + -15k = -7 + 0 -82 + -15k = -7 Add '82' to each side of the equation. -82 + 82 + -15k = -7 + 82 Combine like terms: -82 + 82 = 0 0 + -15k = -7 + 82 -15k = -7 + 82 Combine like terms: -7 + 82 = 75 -15k = 75 Divide each side by '-15'. k = -5 Simplifying k = -5
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