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Simplifying -45 = -7(-3 + 6k) + -2(5k + 7) -45 = (-3 * -7 + 6k * -7) + -2(5k + 7) -45 = (21 + -42k) + -2(5k + 7) Reorder the terms: -45 = 21 + -42k + -2(7 + 5k) -45 = 21 + -42k + (7 * -2 + 5k * -2) -45 = 21 + -42k + (-14 + -10k) Reorder the terms: -45 = 21 + -14 + -42k + -10k Combine like terms: 21 + -14 = 7 -45 = 7 + -42k + -10k Combine like terms: -42k + -10k = -52k -45 = 7 + -52k Solving -45 = 7 + -52k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '52k' to each side of the equation. -45 + 52k = 7 + -52k + 52k Combine like terms: -52k + 52k = 0 -45 + 52k = 7 + 0 -45 + 52k = 7 Add '45' to each side of the equation. -45 + 45 + 52k = 7 + 45 Combine like terms: -45 + 45 = 0 0 + 52k = 7 + 45 52k = 7 + 45 Combine like terms: 7 + 45 = 52 52k = 52 Divide each side by '52'. k = 1 Simplifying k = 1
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