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Simplifying 7k + 2(k + -5) = 7(k + -2) + 8 Reorder the terms: 7k + 2(-5 + k) = 7(k + -2) + 8 7k + (-5 * 2 + k * 2) = 7(k + -2) + 8 7k + (-10 + 2k) = 7(k + -2) + 8 Reorder the terms: -10 + 7k + 2k = 7(k + -2) + 8 Combine like terms: 7k + 2k = 9k -10 + 9k = 7(k + -2) + 8 Reorder the terms: -10 + 9k = 7(-2 + k) + 8 -10 + 9k = (-2 * 7 + k * 7) + 8 -10 + 9k = (-14 + 7k) + 8 Reorder the terms: -10 + 9k = -14 + 8 + 7k Combine like terms: -14 + 8 = -6 -10 + 9k = -6 + 7k Solving -10 + 9k = -6 + 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. -10 + 9k + -7k = -6 + 7k + -7k Combine like terms: 9k + -7k = 2k -10 + 2k = -6 + 7k + -7k Combine like terms: 7k + -7k = 0 -10 + 2k = -6 + 0 -10 + 2k = -6 Add '10' to each side of the equation. -10 + 10 + 2k = -6 + 10 Combine like terms: -10 + 10 = 0 0 + 2k = -6 + 10 2k = -6 + 10 Combine like terms: -6 + 10 = 4 2k = 4 Divide each side by '2'. k = 2 Simplifying k = 2
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