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Simplifying -1k(-5) + -1(-2)(-1k + -5) = -2 + -1(-2k + 4) + -3 Reorder the terms for easier multiplication: -1 * -5k + -1(-2)(-1k + -5) = -2 + -1(-2k + 4) + -3 Multiply -1 * -5 5k + -1(-2)(-1k + -5) = -2 + -1(-2k + 4) + -3 Reorder the terms: 5k + -1 * -2(-5 + -1k) = -2 + -1(-2k + 4) + -3 Multiply -1 * -2 5k + 2(-5 + -1k) = -2 + -1(-2k + 4) + -3 5k + (-5 * 2 + -1k * 2) = -2 + -1(-2k + 4) + -3 5k + (-10 + -2k) = -2 + -1(-2k + 4) + -3 Reorder the terms: -10 + 5k + -2k = -2 + -1(-2k + 4) + -3 Combine like terms: 5k + -2k = 3k -10 + 3k = -2 + -1(-2k + 4) + -3 Reorder the terms: -10 + 3k = -2 + -1(4 + -2k) + -3 -10 + 3k = -2 + (4 * -1 + -2k * -1) + -3 -10 + 3k = -2 + (-4 + 2k) + -3 Reorder the terms: -10 + 3k = -2 + -4 + -3 + 2k Combine like terms: -2 + -4 = -6 -10 + 3k = -6 + -3 + 2k Combine like terms: -6 + -3 = -9 -10 + 3k = -9 + 2k Solving -10 + 3k = -9 + 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 + 3k + -2k = -9 + 2k + -2k Combine like terms: 3k + -2k = 1k -10 + 1k = -9 + 2k + -2k Combine like terms: 2k + -2k = 0 -10 + 1k = -9 + 0 -10 + 1k = -9 Add '10' to each side of the equation. -10 + 10 + 1k = -9 + 10 Combine like terms: -10 + 10 = 0 0 + 1k = -9 + 10 1k = -9 + 10 Combine like terms: -9 + 10 = 1 1k = 1 Divide each side by '1'. k = 1 Simplifying k = 1
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