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Simplifying 7 + -7(2k + -5) + 2x = 9k + -1(k + -2) Reorder the terms: 7 + -7(-5 + 2k) + 2x = 9k + -1(k + -2) 7 + (-5 * -7 + 2k * -7) + 2x = 9k + -1(k + -2) 7 + (35 + -14k) + 2x = 9k + -1(k + -2) Combine like terms: 7 + 35 = 42 42 + -14k + 2x = 9k + -1(k + -2) Reorder the terms: 42 + -14k + 2x = 9k + -1(-2 + k) 42 + -14k + 2x = 9k + (-2 * -1 + k * -1) 42 + -14k + 2x = 9k + (2 + -1k) Reorder the terms: 42 + -14k + 2x = 2 + 9k + -1k Combine like terms: 9k + -1k = 8k 42 + -14k + 2x = 2 + 8k Solving 42 + -14k + 2x = 2 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. 42 + -14k + -8k + 2x = 2 + 8k + -8k Combine like terms: -14k + -8k = -22k 42 + -22k + 2x = 2 + 8k + -8k Combine like terms: 8k + -8k = 0 42 + -22k + 2x = 2 + 0 42 + -22k + 2x = 2 Add '-42' to each side of the equation. 42 + -22k + -42 + 2x = 2 + -42 Reorder the terms: 42 + -42 + -22k + 2x = 2 + -42 Combine like terms: 42 + -42 = 0 0 + -22k + 2x = 2 + -42 -22k + 2x = 2 + -42 Combine like terms: 2 + -42 = -40 -22k + 2x = -40 Add '-2x' to each side of the equation. -22k + 2x + -2x = -40 + -2x Combine like terms: 2x + -2x = 0 -22k + 0 = -40 + -2x -22k = -40 + -2x Divide each side by '-22'. k = 1.818181818 + 0.09090909091x Simplifying k = 1.818181818 + 0.09090909091x
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