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Simplifying 7(4 + 7k) + -3 = 1 + 5(6 + 10k) (4 * 7 + 7k * 7) + -3 = 1 + 5(6 + 10k) (28 + 49k) + -3 = 1 + 5(6 + 10k) Reorder the terms: 28 + -3 + 49k = 1 + 5(6 + 10k) Combine like terms: 28 + -3 = 25 25 + 49k = 1 + 5(6 + 10k) 25 + 49k = 1 + (6 * 5 + 10k * 5) 25 + 49k = 1 + (30 + 50k) Combine like terms: 1 + 30 = 31 25 + 49k = 31 + 50k Solving 25 + 49k = 31 + 50k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-50k' to each side of the equation. 25 + 49k + -50k = 31 + 50k + -50k Combine like terms: 49k + -50k = -1k 25 + -1k = 31 + 50k + -50k Combine like terms: 50k + -50k = 0 25 + -1k = 31 + 0 25 + -1k = 31 Add '-25' to each side of the equation. 25 + -25 + -1k = 31 + -25 Combine like terms: 25 + -25 = 0 0 + -1k = 31 + -25 -1k = 31 + -25 Combine like terms: 31 + -25 = 6 -1k = 6 Divide each side by '-1'. k = -6 Simplifying k = -6
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