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Simplifying 7(k + -6) + -1(-9k + -2) = 15k Reorder the terms: 7(-6 + k) + -1(-9k + -2) = 15k (-6 * 7 + k * 7) + -1(-9k + -2) = 15k (-42 + 7k) + -1(-9k + -2) = 15k Reorder the terms: -42 + 7k + -1(-2 + -9k) = 15k -42 + 7k + (-2 * -1 + -9k * -1) = 15k -42 + 7k + (2 + 9k) = 15k Reorder the terms: -42 + 2 + 7k + 9k = 15k Combine like terms: -42 + 2 = -40 -40 + 7k + 9k = 15k Combine like terms: 7k + 9k = 16k -40 + 16k = 15k Solving -40 + 16k = 15k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-15k' to each side of the equation. -40 + 16k + -15k = 15k + -15k Combine like terms: 16k + -15k = 1k -40 + 1k = 15k + -15k Combine like terms: 15k + -15k = 0 -40 + 1k = 0 Add '40' to each side of the equation. -40 + 40 + 1k = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 1k = 0 + 40 1k = 0 + 40 Combine like terms: 0 + 40 = 40 1k = 40 Divide each side by '1'. k = 40 Simplifying k = 40
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