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Simplifying 7k + 19(5 + 2k) = 3k + -1(k + -4) 7k + (5 * 19 + 2k * 19) = 3k + -1(k + -4) 7k + (95 + 38k) = 3k + -1(k + -4) Reorder the terms: 95 + 7k + 38k = 3k + -1(k + -4) Combine like terms: 7k + 38k = 45k 95 + 45k = 3k + -1(k + -4) Reorder the terms: 95 + 45k = 3k + -1(-4 + k) 95 + 45k = 3k + (-4 * -1 + k * -1) 95 + 45k = 3k + (4 + -1k) Reorder the terms: 95 + 45k = 4 + 3k + -1k Combine like terms: 3k + -1k = 2k 95 + 45k = 4 + 2k Solving 95 + 45k = 4 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 95 + 45k + -2k = 4 + 2k + -2k Combine like terms: 45k + -2k = 43k 95 + 43k = 4 + 2k + -2k Combine like terms: 2k + -2k = 0 95 + 43k = 4 + 0 95 + 43k = 4 Add '-95' to each side of the equation. 95 + -95 + 43k = 4 + -95 Combine like terms: 95 + -95 = 0 0 + 43k = 4 + -95 43k = 4 + -95 Combine like terms: 4 + -95 = -91 43k = -91 Divide each side by '43'. k = -2.11627907 Simplifying k = -2.11627907
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