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Simplifying 14 = -5(k + 1) + -7(7k + 5) Reorder the terms: 14 = -5(1 + k) + -7(7k + 5) 14 = (1 * -5 + k * -5) + -7(7k + 5) 14 = (-5 + -5k) + -7(7k + 5) Reorder the terms: 14 = -5 + -5k + -7(5 + 7k) 14 = -5 + -5k + (5 * -7 + 7k * -7) 14 = -5 + -5k + (-35 + -49k) Reorder the terms: 14 = -5 + -35 + -5k + -49k Combine like terms: -5 + -35 = -40 14 = -40 + -5k + -49k Combine like terms: -5k + -49k = -54k 14 = -40 + -54k Solving 14 = -40 + -54k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '54k' to each side of the equation. 14 + 54k = -40 + -54k + 54k Combine like terms: -54k + 54k = 0 14 + 54k = -40 + 0 14 + 54k = -40 Add '-14' to each side of the equation. 14 + -14 + 54k = -40 + -14 Combine like terms: 14 + -14 = 0 0 + 54k = -40 + -14 54k = -40 + -14 Combine like terms: -40 + -14 = -54 54k = -54 Divide each side by '54'. k = -1 Simplifying k = -1
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