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Simplifying 5(2x + 3) + -5 = 2(5x + k) + -2 Reorder the terms: 5(3 + 2x) + -5 = 2(5x + k) + -2 (3 * 5 + 2x * 5) + -5 = 2(5x + k) + -2 (15 + 10x) + -5 = 2(5x + k) + -2 Reorder the terms: 15 + -5 + 10x = 2(5x + k) + -2 Combine like terms: 15 + -5 = 10 10 + 10x = 2(5x + k) + -2 Reorder the terms: 10 + 10x = 2(k + 5x) + -2 10 + 10x = (k * 2 + 5x * 2) + -2 10 + 10x = (2k + 10x) + -2 Reorder the terms: 10 + 10x = -2 + 2k + 10x Add '-10x' to each side of the equation. 10 + 10x + -10x = -2 + 2k + 10x + -10x Combine like terms: 10x + -10x = 0 10 + 0 = -2 + 2k + 10x + -10x 10 = -2 + 2k + 10x + -10x Combine like terms: 10x + -10x = 0 10 = -2 + 2k + 0 10 = -2 + 2k Solving 10 = -2 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 10 + -2k = -2 + 2k + -2k Combine like terms: 2k + -2k = 0 10 + -2k = -2 + 0 10 + -2k = -2 Add '-10' to each side of the equation. 10 + -10 + -2k = -2 + -10 Combine like terms: 10 + -10 = 0 0 + -2k = -2 + -10 -2k = -2 + -10 Combine like terms: -2 + -10 = -12 -2k = -12 Divide each side by '-2'. k = 6 Simplifying k = 6
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