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Simplifying 7(k + -7) + -1(-9k + -7) = 15k Reorder the terms: 7(-7 + k) + -1(-9k + -7) = 15k (-7 * 7 + k * 7) + -1(-9k + -7) = 15k (-49 + 7k) + -1(-9k + -7) = 15k Reorder the terms: -49 + 7k + -1(-7 + -9k) = 15k -49 + 7k + (-7 * -1 + -9k * -1) = 15k -49 + 7k + (7 + 9k) = 15k Reorder the terms: -49 + 7 + 7k + 9k = 15k Combine like terms: -49 + 7 = -42 -42 + 7k + 9k = 15k Combine like terms: 7k + 9k = 16k -42 + 16k = 15k Solving -42 + 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. -42 + 16k + -15k = 15k + -15k Combine like terms: 16k + -15k = 1k -42 + 1k = 15k + -15k Combine like terms: 15k + -15k = 0 -42 + 1k = 0 Add '42' to each side of the equation. -42 + 42 + 1k = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 1k = 0 + 42 1k = 0 + 42 Combine like terms: 0 + 42 = 42 1k = 42 Divide each side by '1'. k = 42 Simplifying k = 42
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