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Simplifying 9(5 + -1k) + 7 = -7(k + -4) + -5 (5 * 9 + -1k * 9) + 7 = -7(k + -4) + -5 (45 + -9k) + 7 = -7(k + -4) + -5 Reorder the terms: 45 + 7 + -9k = -7(k + -4) + -5 Combine like terms: 45 + 7 = 52 52 + -9k = -7(k + -4) + -5 Reorder the terms: 52 + -9k = -7(-4 + k) + -5 52 + -9k = (-4 * -7 + k * -7) + -5 52 + -9k = (28 + -7k) + -5 Reorder the terms: 52 + -9k = 28 + -5 + -7k Combine like terms: 28 + -5 = 23 52 + -9k = 23 + -7k Solving 52 + -9k = 23 + -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. 52 + -9k + 7k = 23 + -7k + 7k Combine like terms: -9k + 7k = -2k 52 + -2k = 23 + -7k + 7k Combine like terms: -7k + 7k = 0 52 + -2k = 23 + 0 52 + -2k = 23 Add '-52' to each side of the equation. 52 + -52 + -2k = 23 + -52 Combine like terms: 52 + -52 = 0 0 + -2k = 23 + -52 -2k = 23 + -52 Combine like terms: 23 + -52 = -29 -2k = -29 Divide each side by '-2'. k = 14.5 Simplifying k = 14.5
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