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Simplifying 2(4 + -1k) + -1(-3)(k + -5) = -1(3k + -5) (4 * 2 + -1k * 2) + -1(-3)(k + -5) = -1(3k + -5) (8 + -2k) + -1(-3)(k + -5) = -1(3k + -5) Reorder the terms: 8 + -2k + -1 * -3(-5 + k) = -1(3k + -5) Multiply -1 * -3 8 + -2k + 3(-5 + k) = -1(3k + -5) 8 + -2k + (-5 * 3 + k * 3) = -1(3k + -5) 8 + -2k + (-15 + 3k) = -1(3k + -5) Reorder the terms: 8 + -15 + -2k + 3k = -1(3k + -5) Combine like terms: 8 + -15 = -7 -7 + -2k + 3k = -1(3k + -5) Combine like terms: -2k + 3k = 1k -7 + 1k = -1(3k + -5) Reorder the terms: -7 + 1k = -1(-5 + 3k) -7 + 1k = (-5 * -1 + 3k * -1) -7 + 1k = (5 + -3k) Solving -7 + 1k = 5 + -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. -7 + 1k + 3k = 5 + -3k + 3k Combine like terms: 1k + 3k = 4k -7 + 4k = 5 + -3k + 3k Combine like terms: -3k + 3k = 0 -7 + 4k = 5 + 0 -7 + 4k = 5 Add '7' to each side of the equation. -7 + 7 + 4k = 5 + 7 Combine like terms: -7 + 7 = 0 0 + 4k = 5 + 7 4k = 5 + 7 Combine like terms: 5 + 7 = 12 4k = 12 Divide each side by '4'. k = 3 Simplifying k = 3
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