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Simplifying 7(1 + -3k) = -7(1 + k) (1 * 7 + -3k * 7) = -7(1 + k) (7 + -21k) = -7(1 + k) 7 + -21k = (1 * -7 + k * -7) 7 + -21k = (-7 + -7k) Solving 7 + -21k = -7 + -7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7k' to each side of the equation. 7 + -21k + 7k = -7 + -7k + 7k Combine like terms: -21k + 7k = -14k 7 + -14k = -7 + -7k + 7k Combine like terms: -7k + 7k = 0 7 + -14k = -7 + 0 7 + -14k = -7 Add '-7' to each side of the equation. 7 + -7 + -14k = -7 + -7 Combine like terms: 7 + -7 = 0 0 + -14k = -7 + -7 -14k = -7 + -7 Combine like terms: -7 + -7 = -14 -14k = -14 Divide each side by '-14'. k = 1 Simplifying k = 1
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