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Simplifying -7(k + -3) + 5(4k + -5) = 1 + 2k + -5 + -5k Reorder the terms: -7(-3 + k) + 5(4k + -5) = 1 + 2k + -5 + -5k (-3 * -7 + k * -7) + 5(4k + -5) = 1 + 2k + -5 + -5k (21 + -7k) + 5(4k + -5) = 1 + 2k + -5 + -5k Reorder the terms: 21 + -7k + 5(-5 + 4k) = 1 + 2k + -5 + -5k 21 + -7k + (-5 * 5 + 4k * 5) = 1 + 2k + -5 + -5k 21 + -7k + (-25 + 20k) = 1 + 2k + -5 + -5k Reorder the terms: 21 + -25 + -7k + 20k = 1 + 2k + -5 + -5k Combine like terms: 21 + -25 = -4 -4 + -7k + 20k = 1 + 2k + -5 + -5k Combine like terms: -7k + 20k = 13k -4 + 13k = 1 + 2k + -5 + -5k Reorder the terms: -4 + 13k = 1 + -5 + 2k + -5k Combine like terms: 1 + -5 = -4 -4 + 13k = -4 + 2k + -5k Combine like terms: 2k + -5k = -3k -4 + 13k = -4 + -3k Add '4' to each side of the equation. -4 + 4 + 13k = -4 + 4 + -3k Combine like terms: -4 + 4 = 0 0 + 13k = -4 + 4 + -3k 13k = -4 + 4 + -3k Combine like terms: -4 + 4 = 0 13k = 0 + -3k 13k = -3k Solving 13k = -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. 13k + 3k = -3k + 3k Combine like terms: 13k + 3k = 16k 16k = -3k + 3k Combine like terms: -3k + 3k = 0 16k = 0 Divide each side by '16'. k = 0 Simplifying k = 0
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