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Simplifying 5(2(k + -5)) = 3(4(k + 2)) Reorder the terms: 5(2(-5 + k)) = 3(4(k + 2)) 5((-5 * 2 + k * 2)) = 3(4(k + 2)) 5((-10 + 2k)) = 3(4(k + 2)) (-10 * 5 + 2k * 5) = 3(4(k + 2)) (-50 + 10k) = 3(4(k + 2)) Reorder the terms: -50 + 10k = 3(4(2 + k)) -50 + 10k = 3((2 * 4 + k * 4)) -50 + 10k = 3((8 + 4k)) -50 + 10k = (8 * 3 + 4k * 3) -50 + 10k = (24 + 12k) Solving -50 + 10k = 24 + 12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12k' to each side of the equation. -50 + 10k + -12k = 24 + 12k + -12k Combine like terms: 10k + -12k = -2k -50 + -2k = 24 + 12k + -12k Combine like terms: 12k + -12k = 0 -50 + -2k = 24 + 0 -50 + -2k = 24 Add '50' to each side of the equation. -50 + 50 + -2k = 24 + 50 Combine like terms: -50 + 50 = 0 0 + -2k = 24 + 50 -2k = 24 + 50 Combine like terms: 24 + 50 = 74 -2k = 74 Divide each side by '-2'. k = -37 Simplifying k = -37
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