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Simplifying 4(k + -3) + -5(k + 1) = 2 + -3(k + -5) Reorder the terms: 4(-3 + k) + -5(k + 1) = 2 + -3(k + -5) (-3 * 4 + k * 4) + -5(k + 1) = 2 + -3(k + -5) (-12 + 4k) + -5(k + 1) = 2 + -3(k + -5) Reorder the terms: -12 + 4k + -5(1 + k) = 2 + -3(k + -5) -12 + 4k + (1 * -5 + k * -5) = 2 + -3(k + -5) -12 + 4k + (-5 + -5k) = 2 + -3(k + -5) Reorder the terms: -12 + -5 + 4k + -5k = 2 + -3(k + -5) Combine like terms: -12 + -5 = -17 -17 + 4k + -5k = 2 + -3(k + -5) Combine like terms: 4k + -5k = -1k -17 + -1k = 2 + -3(k + -5) Reorder the terms: -17 + -1k = 2 + -3(-5 + k) -17 + -1k = 2 + (-5 * -3 + k * -3) -17 + -1k = 2 + (15 + -3k) Combine like terms: 2 + 15 = 17 -17 + -1k = 17 + -3k Solving -17 + -1k = 17 + -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. -17 + -1k + 3k = 17 + -3k + 3k Combine like terms: -1k + 3k = 2k -17 + 2k = 17 + -3k + 3k Combine like terms: -3k + 3k = 0 -17 + 2k = 17 + 0 -17 + 2k = 17 Add '17' to each side of the equation. -17 + 17 + 2k = 17 + 17 Combine like terms: -17 + 17 = 0 0 + 2k = 17 + 17 2k = 17 + 17 Combine like terms: 17 + 17 = 34 2k = 34 Divide each side by '2'. k = 17 Simplifying k = 17
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