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Simplifying 5(3x + 7) + -1 = 3(5x + k) + 4 Reorder the terms: 5(7 + 3x) + -1 = 3(5x + k) + 4 (7 * 5 + 3x * 5) + -1 = 3(5x + k) + 4 (35 + 15x) + -1 = 3(5x + k) + 4 Reorder the terms: 35 + -1 + 15x = 3(5x + k) + 4 Combine like terms: 35 + -1 = 34 34 + 15x = 3(5x + k) + 4 Reorder the terms: 34 + 15x = 3(k + 5x) + 4 34 + 15x = (k * 3 + 5x * 3) + 4 34 + 15x = (3k + 15x) + 4 Reorder the terms: 34 + 15x = 4 + 3k + 15x Add '-15x' to each side of the equation. 34 + 15x + -15x = 4 + 3k + 15x + -15x Combine like terms: 15x + -15x = 0 34 + 0 = 4 + 3k + 15x + -15x 34 = 4 + 3k + 15x + -15x Combine like terms: 15x + -15x = 0 34 = 4 + 3k + 0 34 = 4 + 3k Solving 34 = 4 + 3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3k' to each side of the equation. 34 + -3k = 4 + 3k + -3k Combine like terms: 3k + -3k = 0 34 + -3k = 4 + 0 34 + -3k = 4 Add '-34' to each side of the equation. 34 + -34 + -3k = 4 + -34 Combine like terms: 34 + -34 = 0 0 + -3k = 4 + -34 -3k = 4 + -34 Combine like terms: 4 + -34 = -30 -3k = -30 Divide each side by '-3'. k = 10 Simplifying k = 10
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