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Simplifying 2(7k + -5) + -5k = 7 + 5(3k + 5) Reorder the terms: 2(-5 + 7k) + -5k = 7 + 5(3k + 5) (-5 * 2 + 7k * 2) + -5k = 7 + 5(3k + 5) (-10 + 14k) + -5k = 7 + 5(3k + 5) Combine like terms: 14k + -5k = 9k -10 + 9k = 7 + 5(3k + 5) Reorder the terms: -10 + 9k = 7 + 5(5 + 3k) -10 + 9k = 7 + (5 * 5 + 3k * 5) -10 + 9k = 7 + (25 + 15k) Combine like terms: 7 + 25 = 32 -10 + 9k = 32 + 15k Solving -10 + 9k = 32 + 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. -10 + 9k + -15k = 32 + 15k + -15k Combine like terms: 9k + -15k = -6k -10 + -6k = 32 + 15k + -15k Combine like terms: 15k + -15k = 0 -10 + -6k = 32 + 0 -10 + -6k = 32 Add '10' to each side of the equation. -10 + 10 + -6k = 32 + 10 Combine like terms: -10 + 10 = 0 0 + -6k = 32 + 10 -6k = 32 + 10 Combine like terms: 32 + 10 = 42 -6k = 42 Divide each side by '-6'. k = -7 Simplifying k = -7
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