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Simplifying -13 = 3(1 + -4k) + -2(k + 1) -13 = (1 * 3 + -4k * 3) + -2(k + 1) -13 = (3 + -12k) + -2(k + 1) Reorder the terms: -13 = 3 + -12k + -2(1 + k) -13 = 3 + -12k + (1 * -2 + k * -2) -13 = 3 + -12k + (-2 + -2k) Reorder the terms: -13 = 3 + -2 + -12k + -2k Combine like terms: 3 + -2 = 1 -13 = 1 + -12k + -2k Combine like terms: -12k + -2k = -14k -13 = 1 + -14k Solving -13 = 1 + -14k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14k' to each side of the equation. -13 + 14k = 1 + -14k + 14k Combine like terms: -14k + 14k = 0 -13 + 14k = 1 + 0 -13 + 14k = 1 Add '13' to each side of the equation. -13 + 13 + 14k = 1 + 13 Combine like terms: -13 + 13 = 0 0 + 14k = 1 + 13 14k = 1 + 13 Combine like terms: 1 + 13 = 14 14k = 14 Divide each side by '14'. k = 1 Simplifying k = 1
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